Suppose that the only information we have about a function f is that f(1) = 5 and the graph of its derivative is as shown: y= ftx] a. Use a linear approximation to estimate f (0.9) and f(1.1). b. Are your estimates in part (a) too large? Or too small? Write a sentence to explain.

Q: .) Write the equation of the normal line of f(x)=2x^2-1/x at x=1? b.) Let y=4x^4+x. At what point…

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

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Q: 4. Determine the point(s) at which the graph of f (x) = has a horizontal tangent. Simplify as much…

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A: Consider the given slope of tangent of the function at x,fx is 2x+6

Q: Compute the derivative of the given function. g(t) = 2t - In(2 – 5t) %3D

A: Given that: g(t)=23t.ln(2-5t)

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Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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A: Given ,  f(x) = √(13 - x) (A)  We have to find the slope of tangent line to the graph of f(x) at the…

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Q: Given that the graph of f(x) passes through the point (7, 3) and that the slope of its tangent line…

A: Use the fact that derivative of a curve is the slope

Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-2x+1 and f(2)=4, then what…

A: The slope of the tangent line to the graph of f(x) at x is m(x)=3x2-2x+1 and f(2)=4.

Q: Find the linear approximation of the function g(x) = 1+x at a = 0 and use it to approximate the…

A: We will find g'(x) using the power rule

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A: Given query is to find the value of f(-4).

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Q: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

Q: Given that the graph of f(x) passes through the point (4, 3) and that the slope of its tangent line…

A: topic - functions

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A: Given that fx=3x21+2x2 Solution :fx=3x21+2x2f'x=6x1+2x2-4x3x21+2x22if…

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Q: Given that the graph of f(x) passes through the point (7, 6) and that the slope of its tangent line…

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Q: If the slope of the tangent line to the graph of y-f(x) at x=a is m(a)=2a+1, and f(1)=5, then what…

A: m(a)= 2 a + 1 f'(x) = m(x) = 2x +1  Integrating f'(x) gives f(x); f(x) = 2(x2/2) + x + c f(x) = x2 +…

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Q: Determine the value(s) of x for which f(x)=9x+8 has a horizontal tangent line.

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Q: If y = f(x) has slope  −4  at x = 3, and y value 5 at x = 3, a) write the formula for the tangent…

A: (a) To write: The formula for the tangent line to f(x) at x=3. Given information:  If y = f(x) has…

Q: What is the equation of the tangent line to the graph of f'(x) at x = 4, if f(x) = vx? O y = - + O y…

A: Topic:- application of derivatives and tangent equation

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: If the slope of the tangent line to the graph of y-f(x) at x-a is m(a)=20+1, and f(1)-5, then what…

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A: Given function is         h(x) = -3x5-5x4+20x3+60x To find the largest slope of h(x) at the tangent…

Q: Find A and B given that the derivative of Ax? + B, x –1 is everywhere continuous.

A: Given function is f(x)=Ax2+B,x&lt;-1Bx5+Ax+4,x≥-1 We have to find the value of A and B  so that the…

Q: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the line…

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Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-x+1  and f(2)=4, then what…

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Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-2x+1 and f(2)=4, then what…

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Q: Determine the value(s) of x for which f(x) = 9x + 8 has a horizontal tangent line

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A: Given : fx = -3x3 -2x2 -1

Q: Given that the graph of f(x)  passes through the point (4,10) and that the slope of its tangent line…

A: Given that the graph of f(x)  passes through the point (4,10) and that the slope of its tangent line…

Q: Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = 3 1- 2x Provide your…

A: see below the answer and explanation

Q: Given that the graph of f(x) passes through the point (5,6) and that the slope of its tangent line…

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Q: Compute f '(x) and find an equation of the tangent line to the graph at x = a. f (x) = x4, a = 2

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Q: Use this definition to compute the derivative of the function at the given value. h(x) = 5x² + 1 X =…

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Q: Compute the derivative of the following function. f(x) = 2 e 2x f'(x) =L %3D

A: To find the derivative

Q: Given that the graph of f(x) passes through the point (5,10) and that the slope of its tangent line…

A: The graph of f(x) passes through the point (5,10) and that the slope of its tangent line at (x,f(x))…

Q: The graph of a function is shown together with the tangent line at a point P. y 5 4 3 2 1 2 3 4 6. 7…

A: topic- tangent

Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1.…

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Q: Given that the graph of f(x) passes through the point (8, 2) and that the slope of its tangent line…

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Q: Find the derivative of the function f(x) = (4x? – a – 4)* at x = - 1. %3D f'(-1) = Pr

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