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MHTCET 10 May 2024 Shift 1 Paper

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Question : 140 of 150

Marks: +1, -0

The approximate value of

x^{3}-2 x^{2}+3 x+2

x=2.01

is

8.07
8.27
8.007
8.17

Solution:

Concept:

Use the approximation formula

f(a+h) \approx f(a) + h\,f'(a)

for a small change

h

.

Explanation:

Let

f(x) = x^{3} - 2x^{2} + 3x + 2

.

Here,

a = 2

and

h = 0.01

.

Differentiate:

f'(x) = 3x^{2} - 4x + 3

.

Compute

f(2) = (2)^{3} - 2(2)^{2} + 3(2) + 2 = 8 - 8 + 6 + 2 = 8

.

Compute

f'(2) = 3(2)^{2} - 4(2) + 3 = 12 - 8 + 3 = 7

.

Using the formula:

f(2.01) \approx 8 + (0.01)(7) = 8 + 0.07 = 8.07

.

Answer:

The approximate value is

8.07

, so the correct option is A.

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