Graph a function y= f(x) that satisfies the following properties: The function f is continuous on (-0,00); f'(-1) = f'(2) = 0; f'(x) >0 on (-1.0) and on (2, 0), while f'(x)<0 on (-0,-1) and on (0,2); and lim f(x)= 0 and lim f(x)=0

Q: Suppose the derivative of a function f is Then f(x) is decreasing on the following interval: ○ (1,4)…

A: A function fx is said to be decreasing on an interval a, b if fx≤fy whenever x≤y and fx is said to…

Q: etch the graph of a function that satisfies all of the given conditions. f'(5) = 0, f'(x) 0 when x…

A: We will find the required graph.

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: Differentiate the function f. Use the form f'(x) = f(x) = 9x² + x + 8 f'(x) = = lim h→0 f(x +h)-f(x)…

A:

Q: f(x) = 2+6x -x'use the limit definition of derivative t

A:

Q: Use the following information to sketch the graph of a continuous function with the following…

A: The given conditions are : (a) f-3=5, f0=2, f3=0 (b) f'x&gt;0 on -∞,-3∪3,∞and f'x&lt;0 on -3,3…

Q: (a) Find the slope m of the tangent to the curve y = 8 + 5x² - 2x³ at the point where x = a. m= (b)…

A:

Q: 1’) Let f be the function f(x) = x^2 +36/x^2 (a) Calculate f'(x) and find all stationary points for…

A: Solution - Given function - f(x)=x2+36x2 a.)        f'(x)=2x+36-2x-2+1             f'(x)=2x-72x…

Q: To write the equation of the line tangent to the curve y = Vx at the point (x, y) = (64, 8), tangent…

A:

Q: Sketch the graph of a function that satisfies all of the given conditions. f'(0) f'(x) > 0 if x 4,…

A:

Q: if f' is continuous, f(3)=0, and f'(3)=7, evaluate lim x to 0 f(3+5x) + f(3+6x)/x

A:

Q: Sketch a graph, f such that f(-2)=4, f(3)=-2, f'(-2)=0, f'(3)=0, f'(x)&gt;0 on (-infinity, 2) and…

A: Given that

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: