Question Type 1: Finding the derivative of a polynomial with different ranges of integers Exercises

Differentiate $f(x) = -4x^4 + 7x^3 - x + 5$.

For $f(x) = 4x^3 - 5x^2 + 6x - 2$, find $f'(x)$ and $f''(x)$.

Find the derivative of the function $f(x)=5x^3+8x^2+9x+3$.

Determine the stationary points of $f(x)=x^4-4x^3+6x^2$.

Find the derivative of $f(x) = 2x^3 - 9x^2 + 4x - 7$.

Given $f(x) = 7x^4 - x^3 + 2x^2 - 5x + 11$, find $f'(2)$.

Find $f'(x)$ if $f(x)=6x^5-3x^2+12$.

Find the equation of the tangent to $y=3x^3-x+2$ at $x=1$.

Find the coordinates of the inflection point(s) of the curve $y = x^3 - 6x^2 + 9x$.

Find all values of $x$ such that the gradient of the curve $y = -2x^5 + 3x^4 - x^2 + x - 4$ is zero.

Let $f(x) = 2x^3 - 3x^2 + 4x + 1$. Find $f'(x)$.

Compute the second derivative of $f(x) = x^5 - 5x^3 + 4x$.