Calculus
Differentiability
What is the average rate of change of the function \(f(x)=6x^2+px+q\) on the interval \([a,b] ?\)
Given the symmetric difference quotient, \[f'(a) \approx \frac{f(a+h)-f(a-h)}{2h}, \] approximate \(f'(2)\) using the symmetric difference quotient for the function \(f(x)=x^4\) with \(h=0.04.\)
What is the average rate of change of the function \(y=2x^2+7\) when the value of \(x\) changes from \(5\) to \(7?\)
What is the slope of the secant line that passes through the two points \((x,f(x))\) on the graph of the function \(f(x)=x^2,\) for \(x=2\) and \(x=2.004?\)
If \(f(x)=-7x+3,\) what is the average rate of change of \(f(x)\) when \(x\) changes from \(4\) to \(7?\)