Q: Find the derivative of the function. t3 2 h(t) : to + 3 h'(t) =
A: Given function: Used formulas: Chain rule of differentiation, Quotient rule of differentiation,…
Q: Find an equation of the tangent line(s) to the graph of the function f that is (are) parallel to the…
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Q: Given f(x) (x – 4)(-5x – 3), find the (x, y)-coordinate on the graph where the tangent line is…
A: For coordinate of horizontal tangent line Differentiation of given function Finding critical point…
Q: Let f(x) = x* – 2x + 14. Then the equation of the tangent line to the graph of f(x) at the point (1,…
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Q: For the following function, make a table of slopes of secant lines and make a conjecture about the…
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Q: Find the point(s) on the graph of the following function where the slope of the tangent line is…
A: Here, the given function can be written as: f(x)=x+7x-7=x-7+14x-7=1+14x-7
Q: Find the equation of the tangent line to the graph of the function f (z) = (22 +9) (z – 3) at the…
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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 fl-1)=2, then what…
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Q: For the function F(x) = [ 2|t|dt, find the tangent lines which are parallel to the bisector of the…
A: 1. Slope of equation is equal to dy/dx 2. Equation of line at point (a, b) and slope = m is :…
Q: Find the slope of the tangent line to the function: 4y 27 1 + х2 At point (1, 1) . 2.
A: Given:
Q: (b) Find the value of k for which 2y +x k is a tangent to the curve y +4x 20. %3D
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Q: For the function P(x) = x3 − 7x, at the point (2, −6), find the following. (a) the slope of the…
A: Instantaneous rate of change of function is slope of tangent at any specific point
Q: Find the points on the graph of f (t) = t 3 - l2t + 4 where the tangent line is horizontal.
A: Now tangent line is horizontal if slope of the tangent line is zero and slope of the tangent line is…
Q: Let f(x) = v16 – x The slope of the tangent line to the graph of f(x) at the point (7, 3) is The…
A: The slope of the tangent line to the given curve is equal to the derivative of the function at the…
Q: For the function y = 6x² + 5x + 6, at the point x = 7, find the following. %3D (a) the slope of the…
A: a) To find the slope of the tangent at x=7, we need dy/dx at x=7
Q: Find the equation of the tangent line to the graph of f (x) = Vx + 169 at the point (0, 13). Answer…
A: We havve to find the equation of the tangent line to the graph off(x) = x+169 at the point (0,13).
Q: Estimate the slope of the tangent line at the point t=−4, for f(t)=15t−6. (Give your answer as a…
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Q: 3xy+ 2yz – 4xz = 3 , (1,1,0)
A: First we find out partial derivatives of given function at given point.and solve it.
Q: Let f(x) = 10 + 2 (0, – 1) is given by y = mx +b for 3e". Then the equation of the tangent line to…
A: Solve for the equation
Q: Find an equation of the line tangent to the following curve at the point (a,f(a)). f(x) = 8 ex + 5x;…
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Q: Use your answer from the last problem to find the slope of the line tangent to f (x) = Vx at x = 9.
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Q: 3. f(エ) = r² +3x
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Q: For the following function, make a table of slopes of secant lines and make a conjecture about the…
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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…
A: Given function is Differentiating both sides , we get
Q: Find the point(s) on the graph of the following function where the slope of the tangent line is…
A:
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 +…
Q: Given that f(10)=10 and f′(10)=4, find an equation for the tangent line to the graph of y=f(x) at…
A: topic - equation of a tangent line
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: "The slope of any tangent to the function f (x) = bª is negative."
A: First we have to find equation of the derivative of the given function.
Q: Find the point(s) on the graph of y = (x2 – 168)e where the tangent line is horizontal.
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Q: Find- for the following function dx x=a(cost + t sint).y=a (sint-tcost)
A: y=a(sint-tcost), x=a(cost+tsint) To find dy/dx.
Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.
A: Consider the provided function, y=5x+2 Find the value of f3 and f'3 at a=3. y=5x+2 We can write…
Q: find the equation of the line tangent to the graph of f at the indicated value of x. f(x)=5e^x, x=0
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Q: Find the slope of the tangent line to the graph of the function at the given point. 4x? + 3y² = 36…
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Q: Find all values of x for which the tangent line of f(x) = V x2 + 18x + 96 is horizontal.
A: Given that, the tangent line horizontal. That is it is parallel to x axis. The equation of the…
Q: Find the equation of the tangent line to the graph of the function f(x) = (22 +6) (z – 3) at the…
A: Fund the equation of the tangent line.
Q: (x) and find the equation of the line tangent t
A: The given figure is f(x)=(2+4x)(3-2x) Here we have to find the f'(x) and the equation of the line…
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Q: What is the slope of the tangent to f(x)=2^(x)+1 at x=2 e. 5.1 f. 1.5 g. 1.5 h. 2.8
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Q: Find the slope of the tangents to the curve at the points (P1 and P2) where it crosses the x-axis.…
A: First find points P1 and P2 and than find the derivative at that points.
Q: Find the equation of the tangent line to the graph of f(x) at the (x, y)-coordinate indicated below.…
A: We have to find the equation of tangent line
Q: Given the function f(x)=e* – e2* Determine the equation of the tangent to f(x) at the point where x…
A: Given query is to find the equation of the tangent to the curve.
Q: What is the slope of the tangent line that touches the graph of In y + e2"- = 3y – 4r at the point…
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Q: Find the slope of the tangent line to the graph of the function at the given point. f(t) = 3t −t2…
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Q: Find an equation of the tangent line to the function y = at the point; 0 P(2). (6) P(4)-
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Q: Find the equation of the tangent line to the function f(x) at the r-value r = 1, and write it in the…
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Q: f (x) = 5cotx, x = ' %3D 4
A: We know slope of tangent line is f'(x) at x= π/4 Equation of tangent line at point (x1,y1) and slope…
Q: Let f(9)=−4 and f′(9)=−4. Then the equation of the tangent line to the graph of y=f(x) at x=9 is:…
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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: The slope of the tangent line to the graph of the function y = 4/T-6 at (36, 18) is | 0 36.00 O0.33…
A: slope is the first derivative of the function with respect to x.
For the following functions and values of a, find ƒ′(a).
b. Determine an equation of the line tangent to the graph of ƒ at the
point (a, ƒ(a)) for the given value of a.
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- Determine all the critical points for the function ?(?) = √?? (?? − ?)In Utah, it is illegal for a person to drive if their blood alcohol level (BAC) is higher than 0.05. For a typical male, their liver can decrease BAC by 0.015 per hour. If a typical male has a BAC of 0.08 at 6pm and consumes no more alcohol, what is his predicted BAC at 7:30pm?When do you predict a typical male in part a. will have a BAC of 0?If Peter had a BAC of 0.08 at 7pm, do you think he will be legal to drive at exactly 9:00pm? Explain your answer in 1-2 sentencesSuppose that a political campaign by Loki estimates that the candidate’s polling percentage yand the amount x (in hundred thousands of pesos) that is spent on television advertising arerelated by y = e^0.3x + (5lnx)^2 while the amount that is spent on social media advertising are related by (x −3)^4 + 3y = x. (a) If P300,000 has been spent on television advertising by Loki’s campaign, determine therate of spending that will increase his polling percentage by 2 percentage points per week. (b) Suppose that Loki’s political adversary, Thor, is slowly ramping up his presence on socialmedia. If Loki’s team plans on spending P400,000 on social media advertising and the rateof spending is at P100,000 per week, at what rate will the polling percentage increase?