Differentiation

Consider the parabola with equation $y=x^2-4x+6$`y`=`x`2−4`x`+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$2`x`−4=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`=−`b`2`a`.

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

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