The velocity of a car is f(t) = 10t meters/second. Use a graph of f(t) to find the exact distance traveled by the car, in meters, from t = 0 tot = 10 seconds. distance = . (include units)

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,…

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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.…

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Q: Using the definition of derivative, find functions: a) y = xVx -2 .2 (b) y =- (x-1)

A: Given ,f(x)=xx2-2Therefore,f(x+h)=(x+h)(x+h)2-2We know that…

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. x-5 f(x) = 6x-1…

A: Here given that f(x)=x-56x-1 We have to find f'(x) and also we have to find the equation of the…

Q: For the function, find the point(s) on the graph at which the tangent line has slope 13. y =…

A: Given: y=-0.025x2+9x To find the slope of tangent we need to differentiate the given curve equation…

Q: h (x) = [ƒ (x)P + g (x), what is the equation of the line tangent to the graph of h at x=-1?

A: Given,           hx=fx2+gx

Q: Find the equation of the tangent line to the graph of ​f(x)=3/x at (9,1/3). The equation of the…

A:

Q: Given the function y=x2cos3x. Find the third-order derivative.

A: To Determine: Third derivative of given function:

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Q: The demand Q for butter is related to the price P by the equation Q. P1/2 = 38. Find dQ/dP by…

A: Given: The given equation is: Q·P12=38

Q: For what value(s) of x does the graph of f(x) = 6x³ + 9x² – 216x %3D e a horizontal tangent?

A: To find the values of x does the graph of fx=6x3+9x2-216x have a horizontal tangent.

Q: Find the derivative of the function using the definition of derivative f(t) = 6.5t2 + 7t

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Q: Given

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Q: Find the derivative of the function. 11 m n'

A: To find the derivative of the given function here we can apply the division rule of differentiation.…

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: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=n

A:

Q: 1. For the function f(x) = 2x? + 7x – 3, - (a). Find the slope of the tangent line at x = 2. [1Mark]…

A: The answers are : (a)  15  (b) y = 15x - 11   The detailed solution is as follows below:

Q: Find an equation of the tangent line to the graph of y = x(x + 3) at the point (1, 1024). 2304x –…

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Q: 213 20 fet)= (9t+3)

A: The given function, f(t)=9t+323

Q: Find an equation for the tangent line to the graph of the function F(x) = V3x2 + 9 at the point (3,…

A: To find the equation of tangent of given equation.

Q: Find an equation for the line tangent to the graph of f(x)=4xe^x at the point (a,f (a)) for a=3…

A:

Q: find the function with the given derivative whosegraph passes through the point P.39. ƒ′(x) = 2x -…

A: We have to find the function for the given derivative passes through the point P: f'x=2x-1, P0, 0…

Q: For the function, find the point(s) on the graph at which the tangent line has slope 2. 1 y=x²-3x²…

A: Given y=13x3-3x2+7x+16 & m=2To find point on the graph: Rules of differentiation: (1)…

Q: For the demand equation, use implicit differentiation to find  dp/dx. 17p2 + 5p + 6 = x

A: Given:

Q: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=7

A:

Q: What is the slope of the tangent line that touches the graph of In y + e2a-1 = 3y – 4x at the point…

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Q: Find an equation of the tangent line to the graph of f at the given point. f(t)= (t -…

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Q: Find the slope of the tangent line to the graph of the function at the given p f(x) = -2x + 6 at…

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Q: Find the derivative f'(-1) for f(t) = 5t3 + 2t? – 1

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Q: Find f(3) if f"(x) = 2 and at the point (2, 6) the slope of the tangent line to f is 10.

A: we have to find f(3) if f"(x) = 2 and at the point (2, 6) the slope of the tangent line to f is 10.

Q: Q4\ Find the slope of the function F(x) = √√x+1 at the point (8,3) And find the equation of the…

A: To find the slope of the function at the given point and also the equation of the tangent line at…

Q: Find the equation of the tangent line to the graph of the function f (2) = (22 +7) (x– 2) at the…

A: Given curve f(x)=(x2+7)(x-2) ⇒f(x)=x3-2x2+7x-14

Q: Find f(3) if f"(x) = 2 and at the point (2,6) the slope of the tangent line to f is 10

A: Given that: f''x=2 At the points the slope of tangent line to the function is 10 So, f'x=10

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx +5 at x-2? %3!

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Q: Find the slope and an equation of the tangent line to the graph of the function f at the specified…

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Q: Let f(x)= e^x^2 . Find an equation of the line tangent to the graph of f at the point the (1,e).

A: Tangent to the graph,

Q: Find an equation of the tangent line to the graph of f(x)=ex​, where x=3.4.   The equation of the…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)= (1 +5x)(3-2x)…

A: topic- derivative and equation of tangent line to function

Q: Find the equation of the tangent line to the graph of the function f (x) = a+3 at the point (0,-).…

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Q: Find the derivative of the function. 8. 7t2 + t

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Q: Q1) A) Find the tangent equation for the function: f(x) = vx2 + 5 at =2 ?

A: The equation of the tangent using the slope intercept is y=mx+b Where 'm' is the slope of line and…

Q: The derivative of the function y = 2* sec(x²) is:

A: I use product rule and chain rule to solve this derivative

Q: Q3 Find the equation of the tangent line to the function f(r) =x+7 at r 1. Show your work.

A: f(x) =x3 +7 Let y = f(x) = x3 +7, we have to find the tangent at x=1 , so value of y at x=1 is  f(1)…

Q: If f(x) = 9x^2 - x^3, find f’(2) and use it it find an equation of the tangent line to the curve y =…

A: Givenf(x)=9x2-x3

Q: Determine the value(s) of x where the slope of the tangent to f(x) = (x – 7)(x² – 5) is –13.

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Q: Find the values of x where the tangent line is horizontal for the function  f(x) = x2(x-5)3

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Q: Q5: Find an equation of the tangent line to the graph of f at (1, 32): y = x (x + 1)5

A: The slope of tangent at any point on the curve is given by the value of derivative of that function…

Q: Find the derivative of the function q=14r-

A: