IBMS Unit 4 Day 2 Practice

Find the derivative function at  $f\left(x\right)=4x^4-5x-3$  .

•  $f'\left(x\right)=16x^3-5$  

•  $f'\left(x\right)=16x^3-5x$  

•  $f'\left(x\right)=16x^3-6$  

•  $f'\left(x\right)=8x^4-6$  

Differentiate the function: $y=-4x^{-5}$  

•  $\frac{\text{d}y}{\text{d}x}=20x^{-4}$  

•  $\frac{\text{d}y}{\text{d}x}=-9x^{-5}$  

•  $\frac{\text{d}y}{\text{d}x}=20x^{-6}$  

•  $\frac{\text{d}y}{\text{d}x}=-20x^{-4}$  

Which of the following is not the same as the term "derivative function"?

• Slope of the tangent line

• Gradient to the curve

• Gradient function

• Instantaneous rate of change

• Average rate of change

 Find the gradient function of the curve: $f\left(x\right)=\frac{3}{x^3}$ 

•  $f'\left(x\right)=-9x^{-4}$  

•  $f'\left(x\right)=3x^{-3}$  

•  $f'\left(x\right)=9x^2$  

•  $f'\left(x\right)=-9x^{-2}$  

What does it mean when you get a positive number as your derivative at a specific point?

• The y-value is positive at that point.

• The function is increasing at that point.

• The function is decreasing at that point.

• The function is neither increasing or decreasing at that point.

At the function $f\left(x\right)=x^2$  , the curve's derivative function is  $f'\left(x\right)=2x$  . 

 At x = 4, the derivative is 8  (ie  $f'\left(4\right)=8$  ).  

At x = 5, the derivative is 10  (ie  $f'\left(5\right)=10$   ).  


Which of the following is true?

• The f(x) value is lower at x = 5.

• The curve is increasing at the same rate at x=4  and x=5.

• The curve is increasing at a faster rate at x = 5.

• The curve is increasing at a faster rate at x = 4.

Given the function $y=5x^{18}$  , find  $\frac{\text{d}y}{\text{d}x}$  when x = 1.

• 5

• 23

• 1,530

• 90

Find the gradient of the curve $y=2x\left(6-3x^2\right)$   at the point (-2, 24 ).

• -420

• -60

• 24

• 84

Point P lies on the curve  $y=3x^2-x+4$  .  The gradient of the curve at point P is equal to 29.  Find the x-coordinate of P.

• 5

• 3.1

• -2.9

• 6

Point T lies on the curve $f\left(x\right)=4x^2+5x$  .  The gradient of the curve at T is equal to -75.  Find the x-coordinate. 

• -8.75

• 6

• -10

• -595