Question

Find the derivative of the function f(x)=2x^2+10 at x=10.

a) f ′ (10)=40
b) f ′ (10)=20
c) f ′ (10)=30
d) f ′ (10)=10

Answer 1

The derivative of the function f(x) = 2x^2 + 10 at x = 10 is f ' (10) = 40.

Step-by-step explanation:

To find the derivative of the function f(x) = 2x^2 + 10 at x = 10, we can use the power rule for differentiation. The power rule states that if f(x) = ax^n, then f'(x) = nax^(n-1). Applying this rule to our function, we have f'(x) = 2(2x)^(2-1) = 4x.

To evaluate the derivative at x = 10, we substitute 10 for x in the expression f'(x) = 4x. Therefore, f'(10) = 4(10) = 40.

So, the correct answer is a) f ' (10) = 40.