tan-1(x) sin x f(x) = 1 for x 0, for x = 0, x²ln(-x)+x+1 for x < 0.

Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: Please answer and show all work thank you!!

A: ## To find a derivative , the equation must only be defined as a function of x , we want to find the…

Q: = x-location(s) of any horizontal tangents to the graph of f(x)= %3D

A: x=-12

Q: Exercise 5: For the following graphs, sketch a graph of the derivative (i.e., you are given f;…

A: Consider the given curve of f(x).

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: The maximum value of directional derivative of f in the direction of b is given by .. (a)Vf.6 (b) Vf…

A: We need to tell the maximum value of the directional derivative of f in the direction of b^.  The…

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: 1- Find the derivative of the following functions: 2 a) ƒ (x) = (√x + 1) (²⁄3 − 2) b) g(t) 3√√x²-1…

A: We have to find the following derivatives.

Q: ах + b (|c| +|d\ #0) cx +d

A:

Q: BIl f(x)=

A:

Q: 17. Determine the derivative of each function. a) y=2(3x-x-1² b) g(x)= /2x + 5

A: We have to find derivative As per guideline we have to solve only three

Q: Let f(x) : x4 Find all values of I such that the slope of the tangent line is - -4.

A: The given function is fx=1x4 and the slope of the tangent line is -4.