NZ Level 7 (NZC) Level 2 (NCEA) Maximums and Minimums Using Calculus (power rule only)

## Interactive practice questions

Consider the parabola with equation $y=x^2-4x+6$y=x24x+6.

a

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$2x4=0.

Solve this equation to find the $x$x-coordinate of the vertex.

b

Find the $x$x-coordinate of the vertex using the formula $x=-\frac{b}{2a}$x=b2a.

c

Find the $y$y-coordinate of the vertex.

d

Which of the following statements is true?

The gradient of the tangent to the parabola is positive at $\left(2,2\right)$(2,2).

A

There is a turning point at $\left(2,2\right)$(2,2).

B

The gradient of the tangent to the parabola is negative at $\left(2,2\right)$(2,2).

C

The gradient of the tangent to the parabola is positive at $\left(2,2\right)$(2,2).

A

There is a turning point at $\left(2,2\right)$(2,2).

B

The gradient of the tangent to the parabola is negative at $\left(2,2\right)$(2,2).

C
Easy
Approx 4 minutes

Consider the parabola with equation $y=5+x-x^2$y=5+xx2.

Consider the parabola with equation $y=2x^2-8x+7$y=2x28x+7.

Consider the function $f\left(x\right)=3x^2-54x+241$f(x)=3x254x+241

### Outcomes

#### M7-10

Apply differentiation and anti-differentiation techniques to polynomials

#### 91262

Apply calculus methods in solving problems