Find slope of the line tangent to the graph of f(x)=x^3−4x+2 at x=2

Answer 1

Find slope of the line tangent to the graph of f(x) = x³ − 4x + 2 at x = 2:

Find the derivative of f(x):

f'(x) = 3x² - 4

Find f'(2), which will be the slope of f(x) at that point:

f'(2) = 3(2)² - 4 = 8

Find f(2) to determine the point that the tangent line must go through:

f(2) = 2³ - 4(2) + 2 = 2

point: (2,2)

Use the point and slope to find the y-intercept (b) of the tangent line:

y = mx + b

2 = 8(2) + b

b = -14

tangent line: y = 8x - 14

Answer 2

f(x) = x³ + 4x + 2, f(2) = 18

f'(x) = 3x² + 4

f'(2) = 3(2)² + 4

f'(2) = 16

y = 16x + b

18 = 16(2) + b

-14 = b

y = 16x - 14