Using the Gradient Function (Derivative)

Using the Gradient Function (Derivative)

12th Grade

7 Qs

quiz-placeholder

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Using the Gradient Function (Derivative)

Using the Gradient Function (Derivative)

Assessment

Quiz

12th Grade

Hard

Created by

Alisha Richardson

Used 2+ times

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7 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Consider the function,
 f(x) = 3x2 + 2x + 5f\left(x\right)\ =\ 3x^2\ +\ 2x\ +\ 5 

Find the gradient function. 

 f(x) = 6x + 2x +5f'\left(x\right)\ =\ 6x\ +\ 2x\ +5  

 f(x) = 6x +2f'\left(x\right)\ =\ 6x\ +2  

 f(x) = 6x2 + 2x f'\left(x\right)\ =\ 6x^2\ +\ 2x\   

 f(x) = 6x + 7f'\left(x\right)\ =\ 6x\ +\ 7  

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Consider the function,
 f(x) = x2 13xf\left(x\right)\ =\ x^2\ -13x 

Find the gradient when x = 0.

 f(0) = 13f'\left(0\right)\ =\ -13  

 f(x) = 2x  13f'\left(x\right)\ =\ 2x\ -\ 13  

 f(0) = 11f'\left(0\right)\ =\ -11  

 f(0) = 0f'\left(0\right)\ =\ 0  

3.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Consider y=5x2y=\frac{5}{x^2}  
Find the gradient when x = -1

 f(1) = 10f'\left(-1\right)\ =\ -10  

 f(1) = 5f'\left(-1\right)\ =\ 5  

 f(x) =10x3f'\left(x\right)\ =\frac{-10}{x^3}  

 f(1) = 10f'\left(-1\right)\ =\ 10  

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Consider the function,
 f(x) =78x2 + 2x3f\left(x\right)\ =7-8x^2\ +\ 2x^3 

Find the gradient function. 

 f(x) = 716x +6x2f'\left(x\right)\ =\ 7-16x\ +6x^2  

 f(x) = 16x +6x2f'\left(x\right)\ =\ -16x\ +6x^2  

 f(x) = 16x2 + 2x3f'\left(x\right)\ =\ -16x^{2\ }+\ 2x^3  

 f(x) = 16x2 +2x2f'\left(x\right)\ =\ -16x^2\ +2x^2  

5.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Consider the total cost,
 C(q) = 8q29C\left(q\right)\ =\ 8q^2-9  
Determine the marginal cost  when q = 10.

 C(10) = 160C'\left(10\right)\ =\ 160  

 C(10) = 151C'\left(10\right)\ =\ 151  

 C(10) = 791C'\left(10\right)\ =\ 791  

 C(10) = 1600C'\left(10\right)\ =\ 1600  

6.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Consider the total cost,
 C(q) = 300 + 5q2C\left(q\right)\ =\ 300\ +\ 5q^2  
Determine the marginal cost  when q =120.

 C(120) = 900C'\left(120\right)\ =\ 900  

 C(120) = 1500C'\left(120\right)\ =\ 1500  

 C(120) = 72,300C'\left(120\right)\ =\ 72,300  

 C(120) = 1200C'\left(120\right)\ =\ 1200  

7.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

A function is defined as, f(x) = x24x  12f\left(x\right)\ =\ x^2-4x\ -\ 12  
Find the value of x on the curve where the gradient is 8.

x = 6

x = 2

x = 0

x = 2.5

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