Q1. Write down the linear (tangent line) approximation to y = e x / 2 at the point x = 0, and sketch the graph of this function and the tangent line.

Q: Find a number a such that the tangent line to the graph v= 3x at x = a is parallel to the tangent…

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Q: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…

A: Slope is derivative of y with respect to x. And equation of tangent is (y-y1) =m(x-x1).

Q: Find (and simplify) the equation of the tangent line to the graph of y = 24 at x = 1.

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Q: For what value of x is the tangent line to the curve y= x2 –6x+5 horizontal?

A: We have to solve the problem

Q: Find an equation for the tangent to the curve f(x) = at (-1 - 1). %3D

A: An equation for the tangent to the curve f(x)=1x3 at (-1,-1)

Q: 4x2 Find the values of x where the tangent line is horizontal for the graph of f(x) = x+2 O A. x=0,…

A: Given: fx=4x2x+2 tangent of given expression will be horizontal, where derivative of given…

Q: Find the equation of the line tangent to the graph of f(x)=(1/8)x3  at x= 3.

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Q: Give an equation for the tangent line to the graph of y = k(x) at the point when x = 2.

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Q: Find the equation of the tangent line to the graph of f(x) = x² – 4 at the point (3, 5). -

A: The equation of the line passing through the point (x1,y1) having slope m is given as (y-y1)…