Differentiation and Integration Quiz

Question 1

Find an expression for the gradient of the function $$f(x) = 4x$$ by differentiating from first principles. 
Answer: [blank_start]4[blank_end]

Accepted Answer

4

Question 2

Which of the following is the derivative of the following equation:
$y= 6x^2 + ^3 \sqrt{4x^2}$

Accepted Answer

$$\frac{dy}{dx}=12x + \frac{8}{3x^3}$$

Answer

$$\frac{dy}{dx}=12x + \frac{8x^3}{3}$$

Answer

$$\frac{dy}{dx}=12x + \frac{8}{3}$$

Question 3

If $x$ represents displacement and $t$ represents time, then which of the following represents acceleration?

Accepted Answer

$x''$

Answer

$ x'(t) $

Answer

$\frac{dx}{dt}$

Question 4

The second order derivative is zero at a local maximum.

Answer

true

Question 5

The derivative of the function $$f(x) = 4x^2 + 5x^3 + 16$$ is given by...

Accepted Answer

$f'(x) = 8x + 15x^2$

Answer

$f'(x) = 12x^3 + 15x^4$

Answer

$f'(x) = 8x + 15x^2 +16$

Question 6

The graph of the derivative of this curve would have which shape?

Question 7

Differentiate the following function:$$f(x) = \frac{3x^2+18x+8}{3x+2}$$.
$f'(x)$ = [blank_start]1[blank_end]

Accepted Answer

1

Question 8

What is the gradient of the normal to the curve $$y= x^4 + 3x^2$$ at the point $(1, 4)$?
The gradient is [blank_start]-1/10[blank_end].

Accepted Answer

-1/10

Question 9

Evaluate the following integral:
$$\int ^5_3 6x^2dx$$
Answer: [blank_start]96[blank_end]

Accepted Answer

96

Questions in this quiz (9)