Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

Find the slope of the tangent to given curve at the indicated point as instructed:

y =\( {x }^{4 } \) - 6\( { x}^{ 3} \) + 13\( { x}^{ 2} \) + 10x + 5 at (0,5) :

Options:

y = 10x + 5

13x + y = 5

x + y = 5

x + 10y = 5

Correct Answer:

y = 10x + 5

Explanation:

Slope of tangent is

$\frac{dy}{dx}=4x^3-18x^2+26x+10$

at (0, 5)

$\frac{dy}{dx}=10$

Equation of tangent is

$y - 5 = 10(x-0)$

$y=10x+5$