Find the Critical Points f(x)=e^t-t( f(x)=e^t-t) 相关知识点: 试题来源: 解析 The function declaration ( f(x)) varies according to ( x), but the input function( e^t-t) only contains the variable( t). Assume ( f(t)=e^t-t). ( f(t)=e^t-t) Find the derivative. (...
(-∞,0)U(0,∞)Set-Builder Notation:{tt≠0Substitute the values of t which cause the derivative to be undefined into the original equation.f()=5()+(0)Solve.f(0)=0T he critical points of a function are where the value of t makes the derivativeo or undefined.(-2,5(-2)}...
Find the critical points. f(x)=3x(16−x)3 Finding Critical Points The critical points of a function can be found through differentiation. Specifically, given a function f(x), the critical points occur at those values of x that satisfy f′(x)=0 or that make f′(x) undefined. Answe...
This lesson explores what critical points are in calculus. It gives a step-by-step explanation of how to find the critical points of a function, and it explains the significance of these points. Related to this Question Explore our homework questions and answ...
Critical Point Examples Example 1:Find the critical points of the function f(x) = x2/3. Solution: The given function is f(x) = x2/3. Its derivative is, f '(x) = (2/3) x-1/3= 2 / (3x1/3) Setting f'(x) = 0, we get 2 / (3x1/3) = 0 ⇒ 2 = 0, which can...
Find the derivative. ( 3t^2+6t) Set the derivative equal to ( 0). ( 3t^2+6t=0) Solve for ( t). ( t=0,-2) Substitute the values of ( x) which cause the derivative to be ( 0) into the original function. ( f(0)=((0))^3+3((0))^2) ( f(-2)=((-2...
Find the Critical Points f(x)=e^(-x^2)( f(x)=e^(-x^2)) 相关知识点: 试题来源: 解析 Find the derivative.( -2e^(-x^2)x)Set the derivative equal to ( 0).( -2e^(-x^2)x=0)Solve for ( x).( x=0)Substitute the values of ( x) which cause the derivative to...
Find the critical points of the given function and then determine whether it is a local maximum, local minimum, or neither.\f(x,y) = 7x^2 + 2xy + 2x +y^2 + y + 4 Find all critical points (x, y) of t...
Find the critical points, points of inflection, local maxima and minima and graph the function: f(x)= x+ tan x on \left ( \frac{-\pi}{2},\frac{\pi}{2} \right ). locate any relative extrema and inflection points of the function y...
Step 1: Find the first derivative f′(x) To find the critical points, we first need to compute the first derivative of the function: f′(x)=ddx(x520−x412+5) Using the power rule of differentiation, we get: f′(x)=5x420−4x312 Simplifying this, we have: f′(x)=x44−x33...