NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Applications of differentiation (logs)

## Interactive practice questions

Consider the function $f\left(x\right)=\ln x$f(x)=lnx.

a

Determine the $x$x value of the $x$x-intercept.

b

Determine the equation of the tangent line to the curve at the point where it crosses the $x$x-axis.

c

Determine the equation of the normal line to the curve at the point where it crosses the $x$x-axis.

Easy
Approx 6 minutes

We want to find the gradient of the curve $y=\ln\left(x^2+5\right)$y=ln(x2+5) at the point where $x=3$x=3.

Consider the function $y=2\ln\left(x^2+e\right)$y=2ln(x2+e).

At the point $\left(a,b\right)$(a,b) on the curve $y=\ln\left(-2x\right)$y=ln(2x), the gradient is $-\frac{1}{3}$13.

Solve for the value of $a$a.

You may use the substitution $u=-2x$u=2x.

### Outcomes

#### M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

#### 91578

Apply differentiation methods in solving problems