Question

Find f ' ( a ) f′(a). f ( x ) = 3 x 2 − 5 x 2 f(x)=3x2-5x 2 f ' ( a )

a) f'(a) = 3a - 5/2
b) f'(a) = 3a² - 5
c) f'(a) = 3a² - 5/2
d) f'(a) = 6a - 5

Answer 1

The derivative of f(x) = 3x^2 - 5x is f'(x) = 6x - 5 using the power rule. Evaluating at the point 'a', the answer is f'(a) = 6a - 5.

Step-by-step explanation:

The question is to find the derivative of the function f(x) = 3x^2 - 5x at the point 'a' which is denoted by f'(a). To find the derivative, we apply the power rule. The power rule states that if you have a function of the form f(x) = x^n, then its derivative f'(x) = n*x^(n-1). Applying this rule to each term of f(x):

• For the term 3x^2, the derivative is 6x.
• For the term -5x, the derivative is -5, since the derivative of x to the power of 1 is 1, and we multiply by the coefficient.

To find the derivative, we use the power rule. The power rule states that if we have a function of the form f(x) = ax^n, the derivative is given by f'(x) = nax^(n-1).

Using the power rule, we have f'(x) = 2 * 3 * x^(2-1) - 1 * 5 * x^(1-1) = 6x - 5.

So, f'(a) = 6a - 5.

Therefore, f'(x) = 6x - 5 and f'(a) = 6a - 5.

So, the correct answer is d) f'(a) = 6a - 5.