Suppose f(x) = 10 - x2. (a) Find the slope of the tangent line to the graph y = f(x) when x = -1. Slope = lim f(ac + h) - f(2) = lim h 0 h h-0 (b) Find an equation for the tangent of to the curve y = f(x) at the point (-1, 9). Tangent line: y = (c) On a piece of paper, sketch the curve y = f(x) and the tangent line together.For f(x) - 2x3 - 3, find f'(x) using the definition f'(x) - lim f(ath) f(2) h f' (2) Using this, find the tangent line to the graph of y = 2x3 - 3 at x = -1. Enter all values as integers, or fractions in lowest terms. yEvaluate the limit below for f(t) = vt and x - 7 in two steps by using algebra to simplify the difference quotient and then evaluating the limit. f (ath) - f(2) lim lim h-0 h\fLet f(ac) = 7vx - 3. If h + 0, then the difference quotient can be simplified as f(x + h) - f(a) A h VBx + Ch+ vx where A, B, and C are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants. A B , and C = Use your answer from above to find f'(x ) - lim f(act h) - f(a) h-0 h Finally, find each of the following: f'(1) = , f' ( 2 ) = , and f'(3) =For f(x) = 2, find f'(x) using the definition f'(x) - lim f(ath)-f(x) ho h f'(z ) = Using this, find the tangent line to the graph of y 2 atx = -1. Write the equation of the line in slope-intercept form. y\fFor f(x) - Vx + 28, find f'(x) using the definition f'(x) = lim f ( * * th ) f ( z ) h -+0 h f ' (2 ) Using this, find the tangent line to the graph of y = Va + 28 at x = -3. Write the equation of the line in slope-intercept form. yYou have answered 1 out of 2 parts correctly. Let f(20 ) = 7+- (a) Find f'(x). f' (20 ) = (b) Find the slope of the tangent line at a - 2. Slope = f'(2) = 13 3x 2 ALet f(x) be the function 5x2 - 8x + 2. Then the difference quotient f ( 4 th ) - f( 4 ) h can be simplified to ah + b for: a and b =Let f(ac) = -4+ 3x2. If h + 0, then the difference quotient can be simplified as f(ath) - f(2) - Ah + Bx + C, h where A, B, and C are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants. A B , and C = Use the simplified expression to find f'(x) = lim f(act h) - f(ac) h Finally, find each of the following: f'(1) , f' ( 2 ) = , and f'(3) =You have answered 3 out of 4 parts correctly. Let f(ac) - 2ac3 + 1. a) Find f(x + h): 2(h+x) +1 b) Find f(x + h) - f(x): 2(h+x)- 2x c) Find f(ath) f(z) . 2x + 1 h h + 2 (h +x) +1 d) Find f'(a): 6.x2Suppose f(t) = - 4 +2 (a) Using the definition of the derivative, calculate the derivative of f. Derivative = f'(t) = lim f (t + h) - f(t) = lim h h-0 (b) Find the values of the derivative at the specified points. f' ( - 2 ) = f' (3) = f' ( V2 ) =

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