Show that the derivative of the function f given by f (x) = 2x³ – 9x² + 12x + 9, at x = 1 and x = 2 are equal.

Question

Show that the derivative of the function f given by f (x) = 2x 3 – 9x 2 + 12x + 9, at x = 1 and x = 2 are equal.

Philoid · Accepted Answer

We are given with a polynomial function f(x) = 2x³ - 9x² + 12x + 9, and we have to find f ‘(x) at x = 1 and x = 2, so by using the formula, f ‘(c) = , we get,

f ‘(1) =

f ‘(1) = lim_x_→₁ 2x² - 7x + 5 = 0

for x = 2, we get,

f ‘(2) =

f ‘(2) = lim_x_→₂ 2x² - 5x + 2 = 0

Hence they are equal at x = 1 and x = 2 .

Show that the derivative of the function f given by f (x) = 2x3 – 9x2 + 12x + 9, at x = 1 and x = 2 are equal.

Show that the derivative of the function f given by f (x) = 2x³ – 9x² + 12x + 9, at x = 1 and x = 2 are equal.