5. Find the slope intercept equation of the line parallel to y = 3x + 1 through the point (4, 5).
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- Magdalen Ward
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2 Rewrite using rational eponents Find the slope intercept equation of the line parallel to y = + 1 through the point (4, 5). 6. Use the limit definition to find the derivative of: g( ) 7. The derivative of a function is the same thing as. (HINT: see Day 1 Notes)
3 Rewrite using rational eponents (8 4 ) Find the slope intercept equation of the line parallel to y = + 1 through the point (4, 5). Slope int : y 7 point slope : y 5 ( 4) 6. Use the limit definition to find the derivative of: g( ) 7. The derivative of a function is the same thing as the SLOPE of a function at a point. 1 ( 5)
4
5
6 f( ) 7 f '( ) 0 g( ) g '( ) 2 h( ) 2 4 h'( ) 8 5 f ( ) f '( ) 15 6
7 If n is a rational number, then the function f() = n is differentiable and d n n d E : f ( ) 5 n 1 d f ( ) 15 d 2 Differentiable means you can take the derivative!
8 The derivative of a constant function is 0. That is, if c is a real number, then d d c 0 E : f( ) 4 f '( ) 0 What type of lines do constants make? Constants are horizontal lines and their slope is zero. Remember, derivatives come from slope.
9 Write answers with only positive whole eponents and radicals! Find each derivative using the power rule. 1. f ( ) f ( ) 7. f( ) 2 4. f( ) g( ) 6. f ( ) 2
10 Write answers with only positive whole eponents and radicals! Find each derivative using the power rule. 1. f ( ) f ( ) f( ) f( ) g( ) 6. f ( )
11 The sum (and difference) of two differentiable functions is differentiable and is the sum (or difference) of their derivatives. d f ( ) g ( ) f '( ) g '( ) d d f ( ) g ( ) f '( ) g '( ) d
12 Write answers with only positive whole eponents and radicals! 7. f ( ) f ( ) 4 5 f ( ) ( ) 2 4 f
13 Write answers with only positive whole eponents and radicals! 7. f ( ) f ( ) f ( ) ( ) 2 4 f
14 The equation for the slope of the line tangent to the curve. Write this down! Is the slope of the line the same as we go across a curve? We can substitute in different -values for our derivative equation to find the slope at specific points.
15 Question 1: Slope of a graph at a specific point, c. Find the derivative (difference quotient) then substitute in c for and simplify. Question 2: Finding a formula for the slope at any point on the graph Find the derivative Question : Finding the equation of the tangent line for at a specific point on the graph Use dy y y ( ) 1 1 d
16 Find the slope of the graph of f()= 4 when: a. =-1 b. =0 c. =1 f ()= a. f (-1)= f ()= b. f (0)= f ()= c. f (1)= Remember a derivative is slope!
17 Find the slope of the graph of f()= 4 when: a. =-1 b. =0 c. =1 f ()= 4 f ()= 4 f ()= 4 a. f (-1)= 4 b. f (0)= 0 c. f (1)= 4 Remember a derivative is slope!
18 Given f() = Write the equation of the tangent line at = 2. First, find f (). Then, find f (2). In other words, the derivative of f() is. The slope of the tangent line at = 2 is. Can you find the equation of the tangent line?? *Substitute the -value into the original equation to find y!! You need ( 1, y 1 ) or ( 1, f( 1 ))
19 Given f() = Write the equation of the tangent line at = 2. We could say f () = So we could say f (2) = 17. In other words, the derivative of f() is The slope of the tangent line at = 2 is 17. Can you find the equation of the tangent line?? *Substitute the -value into the original equation to find y!! You need ( 1, y 1 ) or ( 1, f( 1 )) y y 22 17( 2) 17 12
20 1. Find the coordinate point. ( 1, y 1 ) Substitute the given -value into the ORIGINAL function to find the y-value of the point 2. Find the slope of the line. m = slope Take the derivative of the function. Then substitute the given -value into the derivative to find the slope at that point.. Use point-slope formula with the slope and point that you found! y y 1 = m( 1 ) where your point is ( 1, y 1 ) and your m = slope
21 First, find the coordinate pair. Net, find the derivative of the function. f() = Net, find the slope of the tangent line at =. Finally, find the equation of the tangent line at the point (, ).
22 First, find the derivative of the function. f() = f '( ) 4 9 Net, find the slope of the tangent line at =. f '() 4() 9 m Finally, find the equation of the tangent line at the point (, 10). y 10 ( ) y 19
23 E. Find an equation of the tangent line to the graph of f() = 2 when = -2. Remember to write an equation of a line we need slope and a point!
24 E. Find an equation of the tangent line to the graph of f() = 2 when = -2. f ()= 2 m 4 *Substitute the value into the original equation to find y!! Write this down! f ( 2) 4 y 4 4( 2) Remember to write an equation of a line we need slope and a point!
25 Have a great day!
26 Not used Fall 18
(A) when x = 0 (B) where the tangent line is horizontal (C) when f '(x) = 0 (D) when there is a sharp corner on the graph (E) None of the above
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Page 1. These are all fairly simple functions in that wherever the variable appears it is by itself. What about functions like the following, ( ) ( )
Chain Rule Page We ve taken a lot of derivatives over the course of the last few sections. However, if you look back they have all been functions similar to the following kinds of functions. 0 w ( ( tan
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