Recent questions tagged maxima-minima

Let $F:\mathbb R\to\mathbb R$ be a differentiable function such that $F'$ is continuous on $\mathbb R$. The derivative $F'(x)$ is equal to $0$ exactly at $x=-4,-1,3,7$ an...

Consider a differentiable function $f$ whose derivative is given by $f'(x)=e^{-x}(x+2)^2(x-1)(x-3)^3$. Which of the following statements are true?There is a local maximum...

Let $f:\mathbb{R}\to\mathbb{R}$ be differentiable at $x=x^*$. If $f'(x^*)=0$, which of the following statements must be true?$f$ is continuous at $x=x^*$ The tangent line...

Find the minimum value of $f(x,y)=xy+x+y$ subject to $x^2+y^2=1$.$-1$ $-\sqrt{2}$ $-1/2$ $-2$

A company splits $12$ research hours between two tasks. If $x$ hours are spent on task A, then $12-x$ hours are spent on task B. The total difficulty score is $D(x)=x^2+(...

A research team has $60$ hours to divide between technical validation and market validation. If $x$ hours are spent on technical validation, then $60-x$ hours are spent o...

A company models its total production cost by $C(x)=x^2+\frac{16}{x}$, where $x>0$ is the number of units produced in hundreds. Find the minimum possible value of $C(x)$.

Let $f(x)=x^{3}-3 x^{2}+2$ be a function defined on $(-1,3]$.Which of the following statements is/are correct?$f(x)$ has exactly two roots in $[-0.9,0]$.$f(x)$ has a mini...

The maximum value of the function $h(x)=-x^3+2 x^2$ in the interval $[-1,1.5]$ is equal to $\qquad$______ (rounded off to 1 decimal place)

Consider the function given below and pick one or more CORRECT statement(s) from the following choices.$$f(x)=x^3-\frac{15}{2} x^2+18 x+20$$ $f(x)$ has a local minimum at...

Let $x$ be a variable that takes real values, and let $f(x)=x^{3}-3 x$. Which of the following statements is/are true?$f(x)$ has a local maximum at $x=-\sqrt{3}$$f(x)$ ha...