Differentiation

Consider the function $f\left(x\right)=9x^2+18x-16$`f`(`x`)=9`x`2+18`x`−16.

a

State the coordinates of the $y$`y`-intercept.

Give your answer in the form $\left(a,b\right)$(`a`,`b`).

b

Solve for the $x$`x`-value(s) of the $x$`x`-intercept(s).

If there is more than one value, write all of them on the same line, separated by commas.

c

Determine an equation for $f'\left(x\right)$`f`′(`x`).

d

Hence solve for the $x$`x`-coordinate(s) of the stationary point(s).

If there is more than one, write all of them on the same line separated by commas.

e

By completing the table of values, find the gradient of the curve for the following values of $x$`x`:

$x$x |
$-2$−2 | $-1$−1 | $0$0 |
---|---|---|---|

$f'\left(x\right)$f′(x) |
$\editable{}$ | $\editable{}$ | $\editable{}$ |

f

Select the correct statement.

$\left(-1,-25\right)$(−1,−25) is a minimum turning point.

A

$\left(-1,-25\right)$(−1,−25) is a maximum turning point.

B

$\left(-1,-25\right)$(−1,−25) is a minimum turning point.

A

$\left(-1,-25\right)$(−1,−25) is a maximum turning point.

B

g

Draw the graph below.

Loading Graph...

Easy

Approx 8 minutes

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