First Derivative Test Review

What is the derivative of the function $$f(x) = 5x^3$$ ?

If $$f'(-3) = 5$$ , what does this indicate about the function $$f(x)$$ at $$x = -3$$ ?

Calculate the derivative of the function $$f(x) = 5x^3 + \frac{3}{4}x^4$$ .

What is the derivative of the function $$y = x^n$$ ?

Find the derivative of the function $$f(x) = 7x^4$$ .

What does the first derivative test help determine?

If $$f'(x) > 0$$ on an interval, what can be said about the function $$f(x)$$ on that interval?

If $$f'(x) < 0$$ on an interval, what can be said about the function $$f(x)$$ on that interval?

What is the significance of a critical point in relation to the first derivative test?

What does $$f'(-3) = 5$$ imply about the slope of the tangent line at $$x = -3$$ ?