Which of the following is an equation of the line tangent to the graph of \(f(x)=x^4-3x^2 \) at the point where \(f'(x)=5\) ?

Summary Submit Skip Question

$$ f(x)=x^4-3x^2 $$ $$ f'(x)=4x^3-6x $$ $$ 5=4x^3-6x $$

Find the intersection of the graphs \(y=5\) and \(y=4x^3-6x\) in your graphing calculator.

$$ x \approx 1.523 $$

Substitue this \(x\)-coordinate back into the initial equation to find the corresponding \(y\)-coordinate.

$$ f(1.523)=-1.578 $$

Use the point slope equation:

$$ y-(-1.578)=5(x-1.523) $$ $$ \boxed{y=5x-9.193} $$