Use the given graph to estimate the value of each derivative

Use the given graph to estimate the value of each derivative. a. f\'(1) b. f\'(2)

Solution

f\'(x) determines the slope for each point. Use the secant slope (f(b) - f(a))/(b - a) to determine the correct estimate.

a) f\'(1) : draw tangent at x = 1

we understand that tangent passes through these two points if we draw at x = 1 :(1 , 2.75 ) and ( 1.5 , 0)

(f(b) - f(a))/(b - a) = ( 0 -2.75)/( 1.5 - 1) = -5.5

b) f\'(2) : draw tangent at x = 2

we understand that tangent passes through these two points if we draw at x = 2 :( 2 , -1.5) and (1 , 1)

(f(b) - f(a))/(b - a) = (1 + 1.5)/( 1 -2) = -2.5