a. find the derivative of f at x. that is, find f(x). b. find the slope of the tangent line to the graph of…

a. find the derivative of f at x. that is, find f(x). b. find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function. f(x)=3.9x² + 5.7x; x = - 1, x = 4 a. f(x)= (simplify your answer. use integers or decimals for any numbers in the expression.)

a. find the derivative of f at x. that is, find f(x). b. find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function. f(x)=3.9x² + 5.7x; x = - 1, x = 4 a. f(x)= (simplify your answer. use integers or decimals for any numbers in the expression.)

Answer

Explanation:

Step1: Apply power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y'=nax^{n - 1}$. For $f(x)=3.9x^{2}+5.7x$, the derivative of $3.9x^{2}$ is $2\times3.9x^{2 - 1}=7.8x$ and the derivative of $5.7x$ is $5.7x^{1 - 1}=5.7$.

Step2: Combine the derivatives

$f'(x)$ is the sum of the derivatives of its terms. So $f'(x)=7.8x + 5.7$.

Answer:

$7.8x + 5.7$