Question

Nsider the quadratic function f(x)=x² −2x

a. Find the derivative of the function. f ′ (x)=
b. Calculate the following values of the derivative.
i. f ′ (−2)=
ii. f ′ (0)=
iii. f ′ (1)=
c. Calculate the coordinates of the vertex of the parabola. (You can use the derivative to help find the x-coordinate.)
d. Graph the function y=f(x) and draw the tangent lines to the graph at points whose x-coordinates are ⇒∩ and 1

Answer 1

The derivative of the quadratic function f(x) = x² - 2x is 2x - 2. The values of the derivative at -2, 0, and 1 are -6, -2, and 0 respectively.

Step-by-step explanation:

To find the derivative of the quadratic function f(x) = x² - 2x, we can use the power rule of differentiation. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1). Applying this rule to the function, we have:

f'(x) = 2x - 2

To calculate the values of the derivative at different points, we simply substitute the given values of x into the derivative.

i. f'(-2) = 2*(-2) - 2 = -6

ii. f'(0) = 2*0 - 2 = -2

iii. f'(1) = 2*1 - 2 = 0