Maximums and Minimums Using Calculus (power rule only)
Interactive practice questions
Consider the parabola with equation $y=x^2-4x+6$y=x2−4x+6.
The vertex of a parabola is located where the derivative is $0$0. If we set the derivative of the given parabola to $0$0, we get $2x-4=0$2x−4=0.
Solve this equation to find the $x$x-coordinate of the vertex.
Find the $x$x-coordinate of the vertex using the formula $x=-\frac{b}{2a}$x=−b2a.
Find the $y$y-coordinate of the vertex.
Which of the following statements is true?
The gradient of the tangent to the parabola is positive at $\left(2,2\right)$(2,2).
There is a turning point at $\left(2,2\right)$(2,2).
The gradient of the tangent to the parabola is negative at $\left(2,2\right)$(2,2).
Consider the parabola with equation $y=5+x-x^2$y=5+x−x2.
Consider the parabola with equation $y=2x^2-8x+7$y=2x2−8x+7.
Consider the function $f\left(x\right)=3x^2-54x+241$f(x)=3x2−54x+241