Find the gradient of $f\left(x\right)=x^5-3x^4$f(x)=x5−3x4 at the point $\left(3,0\right)$(3,0).

Denote this gradient by $f'\left(3\right)$f′(3).

Find the gradient of $f\left(x\right)=-\frac{27}{x^2}$f(x)=−27x2 at the point $\left(3,-3\right)$(3,−3).

Find the gradient of $f\left(x\right)=\frac{11}{x}+\frac{10}{x^2}$f(x)=11x+10x2 at the point $\left(4,\frac{27}{8}\right)$(4,278).

Denote this gradient by $f'\left(4\right)$f′(4).

Find the gradient of $f\left(x\right)=\frac{6}{\sqrt{x}}$f(x)=6√x at the point $\left(25,\frac{6}{5}\right)$(25,65).

Denote this gradient by $f'\left(25\right)$f′(25).

Apply differentiation and anti-differentiation techniques to polynomials

Apply calculus methods in solving problems