For the function g(x) = sin(ax), find all points – 1 < c < 1 where the MVT shows g(1) – g(-1) = g'(c)(1 – (–1)) (meaning: where the tangent slope is equal to the secant slope).

Q: find an equation of the tangent plane at the given point. f (x, y) = ln(4x2 − y2), (1, 1)

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Q: For the curve xy+ x²y – xy² = 1, use implicit differentiation to find the equations of the tangent…

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Q: Find the equation for the tangent line to the curve y = f(x) at the given x-value. f(x) = (2x + 3)“…

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Q: Find the equation of the tangent line to the curve point (1,0). f(x) = x – e²²-1 at the

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Q: Consider the graph of the function f(x) = ln(1 + x²) for x > 0. 1. Find f'(x). 2. At which value of…

A: Ta which value of x the slope of tangent line the greatest.

Q: Find the slopes of the tangent lines to the graph of f(x) = 2e² at the points (0, 2) and (1, 2e).

A: See the attached file to know how to find thesthe of a tangent at the given points.

Q: Find the equation of the tangent line to the graph of f(x) = In x at xo = e 8.

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = e*…

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Q: Find the equation of the line tangent to the graph of f(x) = 4 sin(x) at a = T.

A: Given,          fx=4sinx at x=π.

Q: Find all value of x=c, so that the tangent line to the graph of f(x) at (c,f(c)) will be horizontal…

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Q: Find the equation of the tangent line to the graph of y = f(x) = 2 tan(x) at the point a = 0.

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Q: Find an equation of the tangent line to the graph of the given function at the specified point. f(x)…

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Q: Find the slope of the tangent line to x2y2+x sin(15y) = 4 at any point (x, y) on the curve.

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = ln(x7/2);…

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Q: 2 Find the equation of the tangent line to the graph of f(x) = at The equation of the tangent line…

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Q: Find an equation of the tangent line to the graph of y = f 1 (x) at x = 3, where f(x) = x 4.

A: Given: f(x)=x4 at x=3  To find the tangent line of the given function at x=3

Q: Find an equation of the tangent line to the curve at the given point. y = x + sin(x), (1, n)

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Q: 1) Find the slope of the line tangent to the curve y = sin x at the point where x=r/3

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Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: Find the equation of the tangent Iline for the function f(x) = at the point x = 1. Write in the form…

A: The objective is to find the equation of the tangent line for the function f(x)=2xx2+1 at the point…

Q: Find an equation of the tangent line to the graph of the function at the given point f(x) = e−x ln…

A: we have to find the equation of the tangent line of the given function at the point (1,0)…

Q: Find the equation of the tangent line to f-l x+4 at the point P (,0) for f(x) = 3x + 3

A: f(x)=(x+4)(3x+3)=x+13(x+1)+33(x+1)=13+1x+1 f'(x)=-1(x+1)2 f''(x)=2(x+1)3 the slope of the tangent at…

Q: Find an equation of the tangent line to the curve at the given point. y = x + sin(x), (T, 1)

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Q: Find an equation of the tangent line to the curve at thegiven point.   y = e2x  Cosπ   x, (0. 1)

A: Given: y=e2xcosπx at 0,1 for finding equation of tangent at given we need slope m of tangent at that…

Q: f (z) = sin (3,/7) at the point 72,0)

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Q: Find a &gt; 0 such that the tangent line to the graph of f (x) = x2e−x at x = a passes through the…

A: The tangent to curve at a point is a line that touches the curve at that point and with a slope…

Q: Determine the equation of the tangent line to the given function at the given value of x. 1) f(x) =…

A: Dear, as per company guidelines we can answer only one question at a time, kindly post other…

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: We have given function  fx=e-xlnx Then, f'x=-e-xlnx+e-x1x=-e-xlnx+e-xx Therefore,…

Q: 4 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph of…

A: We know that if m is slope and (x1,y1) is point on line the equation of line is given as-  (y - y1 )…

Q: 1. (a) Use implicit differentiation to find the slope of the tangent to the curve y? – xy +y + 2 = 0…

A: Given: The equation of the curve y2-xy+y+2=0

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = e=*…

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Q: Find the slope of the tangent line of the function using the given x-value. 7. f(x) = (x² + 4x)(3x²…

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Q: Find the equation for the tangent line to the curve y=f(x) at the give x-value. f(x)=ex^2-1 at x=1

A: equation of the tangent at the point ( x1,y1) with slope  y - y1 = slope ( x - x1)

Q: 7. Apply the appropriate rule to determine the slope of the tangent line to the curve graph given by…

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Q: Find the slope of the tangent line of the function using the given x-value. 7. f(x) = (x² + 4x)(3x²…

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Q: Find the equation of the tangent to the curve y = cos 2x at the point where x = kko

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Q: Find a point of the following curve at which the tangent line has equation = x + T. .2 2.xy –…

A: Given equation of tangent  is     y=x+π⇒ slope of tangent  =1

Q: The tangent plane to the graph of at the point where (x, y) = (2, 2) (write the appropriate function…

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Q: Find an equation of the tangent line to the curve at the given point. y = e* cos(x) + sin(x), (0, 1)

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Q: Find the x-coordinate(s) of the point(s) on the graph of y = x + sinx at which the tangent line has…

A: Graph of y=x+sinx

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: Determine the equation of the curve whose tangent line at any point (x, y) is e* - cos x and passes…

A: We have to find curve

Q: 41. Find the points on the graph of f(x) = 5- 2 sin.x, 0<x 27, at which the tangent line is parallel…

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Q: Find an equation of the tangent line to the graph of the function                    y = esinh x, at…

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = [(x −…

A: Consider the given function.

Q: 3. Find Hhe to the (1,2) slope of the tangent live r=2-sin@ at the point curve

A: Then we plug this in the slope formula of the polar curve

Q: Find an equation of the tangent line to the curve at the given point. y = cos (x² – 2x + 1), (1, 1).

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Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = (2x +…

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Q: Find an equation of the tangent line to the graph of f(x) = 2 + e1−x at the point (1, 3).

A: We have to find equation of tangent line to the graph of function fx=2+e1-x at the point 1, 3. We…

Q: Find the x-coordinate of the point on the graph of y=x^2 where the tangent line is parallel to the…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: