Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives2 Marks
Question
Find the absolute maximum value and the absolute minimum value of the function:
$f(x)=(x-1)^{2}+3, x \in[-3,1]$
✓

Answer

Given that $f(x)=(x-1)^{2}+3, x \in[-3,1]$
$\Rightarrow$ f'(x) = 2(x - 1)
Now, f'(x) = 0
$\Rightarrow$ 2(x - 1) = 0
$\Rightarrow$ x = 1
Now, we evaluate the value of 'f ' at critical point x = 1, and at end points of the interval [-3, 1].
$f(1) = (1 - 1)^2 + 3 = 0 + 3 = 3$
$f(-3) = (-3 - 1)^2 + 3 = 16 + 3 = 19$
Therefore, the absolute maximum value of f on [-3, 1] is 19 occuring at x = -3.
And the absolute minimum value of f on [-3, 1] is 3 occurring at x = 1.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Application of Derivatives→Application of Derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector $3\hat{\text{i}}+5\hat{\text{j}}-6\hat{\text{k}}.$
→
Construct a $2 \times 3$ matrix $A=\left[a_{i j}\right]$ whose elements $a_{i j}$ are give by:
$a_{i j}=i . j$
→
Evalute the following integrals:
$\int\frac{1-\sin\text{x}}{\text{x}+\cos\text{x}}\text{dx}$
→
Write the value of $\tan^{-1}\sqrt3+\cot^{-1}\sqrt3$
→
Find an angle $\theta$
Whose rate of increase twice is twice the rate of decrease of its cosine.
→
Evaluate $\int\frac{\text{x}+\cos6\text{x}}{3\text{x}^2+\sin6\text{x}}\text{ dx}$
→
Find two positive numbers whose sum is $14$ and the sum of whose squares is minimum.
→
Integrate the function: $\frac{{\cos \sqrt x }}{{\sqrt x }}$
→
Find the particular solution of the differential equation $(1 + e^{2x})dy + (1 + y^2)e^x dx = 0,$ given that $y = 1$, when $x = 0.$
→
Differentiate the following w.r.t.x: $\frac{\cos\text{x}}{\log\text{x}},\text{x}>0$
→