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if y(x)=Power[x,2]+3 and x(t)=3t-1, what is y(x(t))??? and how does functional notation make sense?? and what are functions????
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- Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x)=2x2+5x-3, a=-0.9find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. 1. ƒ(x) = x2 + 2x, a = 0.1 2. ƒ(x) = x-1, a = 0.9 3. ƒ(x) = 2x2 + 3x - 3, a = -0.9 4. ƒ(x) = 1 + x, a = 8.11. Find the derivative of the expanded function a. a^2x^2+2abx+b^2 b. a^2x^4+2abx^3+2acx^2+b^2x^2+2bcx+c^2 2. Find the derivative by chain rule a. (ax+b)^2 b.(ax^2+bx+c)^2
- The function f(x)=2x^3−42x^2+270x+8has derivative f′(x)=6x^2-84x+270.f(x) has one local minimum and one local maximum.f(x) has a local minimum at x equals_______, with value ________ and a local maximum at x equals _____ with value ________Use algebraic methods to determine the critical value(s) of f(x)= x/(x^2-x-2). Give your answers in exact form.Use algebraic methods to determine the critical value(s) of f(x) = x √4−x. Give your answers in exact form.
- Solve for the derivative of the given functions using the Chain Ruleformula. Let f(x) = √(x2 + 3x + 1). Find f′(x). a.) What is the inner and the outer functions?b.) What is the derivative of the inner function?c.) What is the derivative of the outer function evaluated at the inner function?A. Find the derivative of a composite function using the Chain Rule or General Power Rule. 1.) y=(3x+1)³ 2.) y=2(2x+1)⁴ 3.) y= √(3-t) 4.) y= 1/(x-1) 5.) y= x/(√x²-1) 6.) y= ((2x+1)²+1)³ 7.) y=^3√(2x+3) 8.) y= (3x+1)⅔Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and second derivative tests. How do I set this problem up and solve it?