Use linear approximation, i.e. the tangent line, to approximate 3√64.4 as follows: Let f(x)=3√x. The equation of the tangent line to f(x) at x=64 can be written in the form y=mx+b.  m= b=  our approximation for 3√64.4 is

Q: 7. Find the equation of the tangent line to the graph of the function 4xy + 5 In y = 28 at the point…

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Q: Find the derivative using the following information.

A: Equation of tangent to curve g(x) at x=2 is y=-3x+2. Its slope is m=-3. Since slope of tangent to…

Q: find the equation of the tangent line at x=-6 for f(x)=x^3/2. write the answer in the form y=mx+b

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Q: (a) If F(x) = 12x/(3 + x²), find F '(3) and use it to find an equation of the tangent line to the…

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Q: Given f(x) =x(4/x), find its tangent line at (1,1).

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Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…

A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…

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. Determine the point (a, la)) for which f'(a) = a, given that Ax) = -x + 3x-7. b. Write the…

A: For (a), Given: We need to find the point a for which f'(a)=a. Here, f'(x)=-2x+3. So,…

Q: Find the equation of the tangent line at the point 0, In 3 3 for f(x)=In 3 e²x² 2e +e²x

A: Topic:- application of derivatives

Q: Given that f(2) =-7 and f'(2) = -8, find an equation for the tangent line to the graph of y = f(x)…

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Q: The product of all the values of x for which the tangent lines to the graph of y= are parallel to…

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Q: If f(x) = x° – 5x + 1, find f'(1) f'(1) = Use it to find an equation of the tangent line to the…

A: Given function, fx=x3-5x+1 Tangent is passing through (x1,y1) (1,-3).

Q: Find all values of x for which the tangent line of f(x) x2 + 18x + 96 is horizontal.

A: fx=x2+18x+96 Differentiating with respect to x, we get f'x=ddxx2+18x+96=12x2+18x+96·dx2+18x+96dx…

Q: For what values of x is the tangent line of the graph of f(x) = 2x – 6x² – 48x + 18 %3D parallel to…

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Q: Find the equation of the tangent line at x = 2 for f(x) = 4+x-2x²-3x³. Write the answer in the form…

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Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: If f(x) = 3x² – 7x + 2, find f'(1). 3x – 7x + 2 at the point (1, – 2). Use this to find the equation…

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Q: The tangent line to the graph of y = In(2x) is perpendicular to x + 4y = 1 at the point where…

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Q: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

Q: Use linear approximation, i.e. the tangent line, to approximate 2.9° as follows: Let f(x) x'. Find…

A: The equation of the tangent to the function is given by the formula , The derivative of the function…

Q: For which value(s) of x does f(x)=4x33+2x2+7x−21 have a tangent line of slope 6? Select all correct…

A: we have to find value of  x at which f'(x)=6

Q: 2 is: The slope of the tangent line to the curve y = - at the point 3, x The equation of this…

A: We have to find out the slope

Q: Use linear approximation, i.e. the tangent line, to approximate 2.8' as follows: Let f(x) = x". The…

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Q: Given that f(2)=−3 and f′(2)=6, find an equation for the tangent line to the graph of y=f(x) at x=2.

A: For the function y=f(x), slope of the tangent at any point (a, f(a)) is given by mT=f'(x) at (a,…

Q: Find the equation of the line tangent to the curve x^3 - 3xy + 4x = 2 at x = 1.

A: On solving this we will get

Q: The tangent line to the graph of y = In(2x) is perpendicular to x + 4y = 1 at the point where…

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Q: tangent

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Q: Let f(x) tangent line to the graph of f(x) at the point (0, given by y = mx + b for 4x + 10 – 19e".…

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Q: Let Q(t) = t2. Find a formula for the slope of the secant line over theinterval [1, t] and use it to…

A: the slope of the secant line over the interval [1, t]

Q: Find the value of 'a' for which the tangent to the curve f(x) = (a + 2) x³ − 3ax² +9ax - 1 never…

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Q: Find an equation of the tangent line to the curve

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Q: The equation of the tangent to the curve f(x)=x3−6 which is parallel to −2y+54x−3=0 is...

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Q: Find the value of 'a' for which the tangent to th ƒ(x) = (a + 2) x³ − 3ax² + 9ax - 1 never makes an…

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Q: If f(x) = 2x2 – 2x + 4, find f'(– 4). 2x + 4 at the point (– 4, 44). Use this to find the equation…

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Q: Find all values of x for which the tangent line of f(x) = / x² + 18x+96 is horizontal.

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Q: Given that f(−6)=−6 and f′(−6)=−6, find an equation for the tangent line to the graph of y=f(x) at…

A: We know that slope of tangent line to the graph of y=f(x) at x=a is f'(a) Therefore, slope of…

Q: Find the equation of the tangent line to the function f(x) = 4*(x– 2) at x = 2. (a) y =…

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Q: find equation of both the tangent lines to the elipse x^2+4y^2=36 that pass through the point(12,3)

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Q: Find the equation of a tangent line to the graph of the function g(x)=2x−x2g(x)=2x−x2 that is…

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Q: For what values of x is the tangent line of the graph of f(x) = 6x^3 + 9x^2 −218x   parallel to the…

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Q: Find the slope of the tangent to Ax) = x²e* at the point (1, e). a) e b) 1 c) 3e d) 2 + e

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Q: - Find the value of 'a' for which the tangent to the curve f(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

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Q: Find the equation of the tangent line to f(x) = (36 + 4x²)¯ at x = Use your answer to (a) to…

A: (a) Given,              f(x)=(36+4x2)-12       at  x=0.

Q: Given that f(−5)=−10 and f′(−5)=−2, find an equation for the tangent line to the graph of y=f(x)at…

A: Topic = Functions

Q: What is the slope of the tangent line that touches the graph of In(y) +e2-1=3y – 4x at the point 3 A…

A: We have to choose the correct answer from the given information according to the given information

Q: Find the equation of the tangent line to f(x)=4x+x^−1/2+1 at the point (4,35/2)

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Q: Find an equation of the tangent line at the point indicated. s(t) = In(7 – 3t), t= 1. %3D (t-1)…

A: Following steps help to find equation of line tangent . 1.Find the first derivative of f(x). 2)…

Q: 3. Find the equation of the tangent line to the graph of x²y + 9xy= 162 at the point (-3, 6).

A:

Q: Find the value of 'a' for which the tangent to the curve ƒ(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

A:

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: