Question Type 1: Finding the first order conditions for polynomials up to cubics Exercises

Find the stationary point of $f(x)=x^2-8x+15$.

Find the stationary points of $f(x)=\frac{x^3}{3}+\frac{5x^2}{2}+6x+10$.

Find all critical points of $f(x)=3x^3-6x^2+9x-2$.

Determine the stationary points of $f(x)=-x^3+4x^2-x+1$.

For $f(x)=x^3-3x^2+2$ determine whether each stationary point is a local minimum or maximum.

Find the critical points of $f(x)=x^3e^{-x^2}$.

Find the critical points of $f(x)=\frac{x^2e^x}{x^2+1}$ and approximate real solutions to two decimal places.

For the function $f(x)=x^3e^{-x^2}$ classify each critical point as local min, max or inflection.

Find the critical points of $f(x)=\frac{x^2e^x}{x-1}$ using technology, and give real solutions accurate to two decimal places.

Find the critical point(s) of $f(x)=e^x+x-\ln(x)$ using technology and give your answer to three decimal places.

For $f(x)=\frac{x^2e^x}{x^2+1}$ determine whether each critical point is a local minimum or maximum using a sign chart or technology.

The function $f(x)=e^x+x-\ln(x)$ has a single critical point at $x\approx0.402$. Determine whether it is a local min or max.