Step 1
Choose the right method
What is the best way to start differentiating this function?
Step 2
Differentiate the cubic term
What is the derivative of \(2x^3\)?
Step 3
Differentiate the rest of the function
What is the derivative of \(-3x^2+\frac{x}{2}+7\)?
Step 4
Write the full derivative
Putting the terms together, which expression is \(f'(x)\)?
Step 5
Substitute the given x-value
Which substitution correctly finds the gradient at \(x=-\frac{1}{2}\)?
Step 6
Final gradient
Now simplify the substitution carefully and type the gradient.
\[
f'(x)=6x^2-6x+\frac{1}{2}
\]
\[
f'\left(-\frac{1}{2}\right)=6\left(\frac{1}{4}\right)-6\left(-\frac{1}{2}\right)+\frac{1}{2}
\]
\[
=\frac{6}{4}+3+\frac{1}{2}
\]