Chapter 2 Differentiation (2.2)

Which of the following is not the function for the first order derivative of  $f'\left(x\right)=-\frac{1}{x^2}$ ? 

•  $f\left(x\right)=\frac{1}{x}$  

•  $f\left(x\right)=\frac{1-x}{x}$  

•  $f\left(x\right)=\frac{x+1}{x}$  

•  $f\left(x\right)=\frac{x}{x+1}$  

Given  $y=x^3-6x^2+9x-5$ , the range value of x where  $\frac{dy}{dx}>0\$  is

• x < -3 or x > 1

• x < 1 or x > 3

• -3 < x < -1

• 1 < x < 3

The gradient of the curve $y=\left(3x+2\right)\left(2x-1\right)$ at point (-1, 3) is 

• -11

• -6

• 3

• 9

Which of the following coordinates on the curve $y=2x^2-x-3$ has its gradient of the tangent equal to 7?

•  $\left(-2,-3\right)$  

•  $\left(-2,3\right)$  

•  $\left(2,-3\right)$  

•  $\left(2,3\right)$  

The gradient of the curve $y=ax+\frac{b}{x}$ at the point   $\left(-1,-3\right)$ is -7. Find the values of a and b.

• a = -2, b = 5

• a = -2, b = -5

• a = 2, b = 5

• a = 5, b = 2

The first derivative for the function $f\left(x\right)=\frac{8}{3}\sqrt{2x^3-5}$ is  

•  $\frac{4}{3\sqrt{2x^3-5}}$  

•  $\frac{12x^2}{\sqrt{2x^3-5}}$  

•  $\frac{8x^2}{\sqrt{2x^3-5}}$  

•  $\frac{8x}{\sqrt{2x^3-5}}$  

If $f\left(x\right)=\left(3x-1\right)^{\frac{1}{3}}$ , then the value for  $f'\left(3\right)$ is 

•  $\frac{1}{12}$  

•  $\frac{1}{4}$  

•  $12$  

•  $4$  

Given that $y=\left(2x+3\right)^5\left(x+3\right)^8$ , the value for  $\frac{\text{d}y}{\text{d}x}$ when x = -2 is 

• -4

• -2

• 2

• 3

 If $f\left(x\right)=\frac{3x^2-5}{x+6},$ then  $f\left(0\right)+6f'\left(0\right)$ is 

• 2

• 0

• -1

• -2

Find the gradient of the curve  $y=\frac{2x-1}{5x+3}$  at  $x=-1$ . 

•  $-\frac{11}{64}$  
  

•  $-\frac{11}{4}$  
  

•  $\frac{11}{64}$  
  

•  $\frac{11}{4}$