2015 ONE(d)

Merit
Question
For what value(s) of xx is the tangent to the graph of the function f(x)=x+4x(x−5)f(x)=\frac{x+4}{x(x-5)} parallel to
the xx-axis?

*You must use calculus and show any derivatives that you need to find when solving this
problem.*
Official Answer
f′(x)=x(x−5)−(x+4)(2x−5)x2(x−5)2f'(x)=\dfrac{x(x-5)-(x+4)(2x-5)}{x^2(x-5)^2}

f′(x)=0⇒x(x−5)−(x+4)(2x−5)=0f'(x)=0 \Rightarrow x(x-5)-(x+4)(2x-5)=0

x2−5x−(2x2+3x−20)=0x^2-5x-(2x^2+3x-20)=0

−x2−8x+20=0-x^2-8x+20=0

x2+8x−20=0x^2+8x-20=0

(x+10)(x−2)=0(x+10)(x-2)=0

x=−10x=-10 or x=2x=2
Grading Criteria

Achievement (u)

  • Correct derivative.

Merit (r)

  • Correct solution with correct derivative.

Excellence T1

-

Excellence T2

-
Exam Paper (2015)Assessment Schedule (2015)
Related Questions
2024 THREE(c)Merit

Find the $x$-value(s) of any stationary point(s) on the graph of the function $f(x)=\dfrac{x^2-5x+4...

2024 THREE(d)Merit

Jamie is doing some baking and pouring the flour to form a conical pile. The height o...

2024 TWO(e)Excellence

The graph of the function $y = \dfrac{xe^{3x}}{2x + k}$, where $k$ is a non-zero constant, has a sin...

2024 TWO(c)Merit

Show that $y = \sin(x^2) - \cos(x)$ is a solution to the equation $\dfrac{d^2y}{dx^2} + 4x^2\,y = 2...

2024 ONE(d)Merit

Find the $x$-value(s) of any stationary points on the graph of the function below, and determine the...