Download App

Maxima and Minima — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMaxima and Minima5 Marks
Question
Find the absolute maximum and the absolute minimum value of the following functions in the given intervals:
$f(x) = (x - 1)^2 + 3$ in $[-3, 1]$
✓

Answer

The given function is $f(x) = (x - 1)^2+ 3.$
$\therefore$ $f'(x) = 2(x - 1)$
Now,$f'(x) = 0 \Rightarrow 2(x - 1) = 0 \Rightarrow x = 1$
Then, we evalute the value of f at critical point $x = 1$ and at the end point of the interval $[-3, 1].$
$f(1) = (1 - 1)^2 + 3 = 0 + 3 = 3$
$f(-3) = (-3 - 1)^2 + 3 = 16 + 3 = 19$
Hence, we can conclude that the absolute maximum value of f on $[-3, 1]$ is occurring at $x = -3$ and the 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 "Solve the Following Question.(5 Marks)" from Maxima and Minima→Maxima and Minima — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation $\text{y}-\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}^{2}+\frac{\text{dy}}{\text{dx}}.$
→
Three urns contains $2$ white and $3$ black balls; $3$ white and $2$ black balls and $4$ white and $1$ black ball respectively. One ball is drawn from an urn chosen at random and it was found to be white. Find the probability that it was drawn from the first urn.
→
A printing company prints two types of magazines A and B. The company earns ₹ 10 and ₹ 15 on magazines A and B per copy. These are processed on three machines I, II, III. Magazine A requires 2 hours on Machine I, 5 hours on Machine II and 2 hours on Machine III. Magazine B requires 3 hours on Machine I, 2 hours on Machine II and 6 hours on Machine III. Machines I, II, III are available for 36, 50, 60 hours per week respectively. Formulate the L.P.P. to determine weekly production of A and B, so that the total profit is maximum.
→
Find the particular solution of the differential equation $\frac{\text{dy}}{\text{dx}}=-4\text{xy}^2$ given that $\text{y}=1.$ when $\text{x}=0.$
→
A pair of fair dice is thrown. Let X be the random variable which denotes the minimum of the two numbers which appear. Find the probability distribution, mean and variance of X.
→
Evaluate the following integrals:$\int\limits^{\frac{\pi}{2}}_0\frac{\sqrt{\cot\text{x}}}{\sqrt{\cot\text{x}}+\sqrt{\tan\text{x}}}\text{ dx}$
→
Evaluate the following integrals:$\int_{0}^\limits{1}\frac{1}{1+2\text{x}+2\text{x}^2+2\text{x}^3+\text{x}^4}\text{ dx}$
→
Show that the exponential function $f : R → R$, given by $f(x) = e^x$, is one-one but not onto. What happens if the co-domain is replaced by R + 0R0 + (set of all positive real numbers)?
→
Solve the following initial value problems:
$\frac{\text{dy}}{\text{dx}}+\text{y}\cot\text{x}=2\cos\text{x},\text{ y}\Big(\frac{\pi}{2}\Big)=0$
→
Evaluate : $\int_0^2 \frac{2^x}{2^x\left(1+4^x\right)} \cdot d x$
→