a. find the derivative of f at x. that is, fi...
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:
$7.8x + 5.7$