Consider the function $f\left(x\right)=7-x^2$f(x)=7−x2.
Find an expression for the derivative $f'\left(x\right)$f′(x) using first principles.
Show all steps of working.
Hence calculate the gradient of $f\left(x\right)$f(x) at the point where $x=-1$x=−1.
Consider the function $f\left(x\right)=x^2+3x+4$f(x)=x2+3x+4.
Consider the function $f\left(x\right)=x^3$f(x)=x3.
Consider the function $f\left(x\right)=x^4$f(x)=x4.