If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line tangent to the graph of g(x) at x = -1. (Let x be the independent variable and y be the dependent variable.)

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

A: To find the slope we find y' at x=2 and y=1 so the slope is 2

Q: If the instantaneous rate of change of f(x) at (8, −7) is 9, write the equation of the line tangent…

A: It's given that the instantaneous rate of change  of  f(x) at  (8,-7) is 9 . We have to find the…

Q: If the instantaneous rate of change of f(x) at (5,-9) is 3, write the equation of the line tangent…

A: For equation of tangent, one have to use y-b=m(x-a)Where (a,b) is the point, m is the slope.

Q: For the function y = 5x2 + 4x + 2, at the point x = 5, find the following. (a) the slope of the…

A:

Q: Find an equation for the line tangent to given curve at the given value of x. y=x2−x at x=−3

A:

Q: Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the…

A:

Q: Find an equation of the tangent to the curve y =x In x atthe point  (e, e).

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

Q: Provide the equation of the line tangent to the given function at the specified point g(x)=ln(x^2);…

A: Given : gx = lnx2

Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 2 if g(2) = −3 and g'(2) = 4.…

A:

Q: For f(x)=x5, the instantaneous rate of change is known to be 405 at x=-3. Find the equation of the…

A: y=fx=x5instantaneous have of change is known to be 405 ,or x = -3∴ y=f-3=-35=-243

Q: For f(x)=x5​, the instantaneous rate of change is known to be 5 at x=−1. Find the equation of the…

A:

Q: If the instantaneous rate of change of f(x) at (3, -5) is 9, write the equation of the line tangent…

A:

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: If the instantaneous rate of change of f(x) at (4, −9) is 8, write the equation of the line tangent…

A: From the given statement, the rate of change of f(x) at (4, –9) is 8.That is,  f′(x) = 8.

Q: Find an equation of the line tangent to f(x) at the point |3D 1+e

A: Find slope at given point and then use formula  to find tangent line

Q: Let f(x) = 6x2 Зх. (a) Find the instantaneous rate of change of f(x) at x = -1. (b) Find the slope…

A: Given the functionf(x)=6x2−3x

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: If the instantaneous rate of change of fx) at (9, -6) is 2, write the equation of the line tangent…

A:

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

A: Our Aim is to find an equation of the tangent line to the graph of the function f(x)=e-x-6-(i) at…

Q: For f(x)=x3​, the instantaneous rate of change is known to be 3 at x=−1. Find the equation of the…

A:

Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: For the function y = (x² + 4)(x - 9x), at (-3, 0) find the following. (a) the slope of the tangent…

A: Given:         y= (x2+ 4)(x3- 9x)

Q: 3. For the fiunction g(x) = x - 2x² –1, at what tangent point(s) is the instantaneous rate of change…

A: given function :

Q: Find an equation of the tangent to the curve  y= x ln x at the point (e ,e )

A: Given: y=xlnx, e,e for finding equation of tangent, we need slopem of tangent at given pointe,e we…

Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: Slope of tangent line is ½. So the equation is of the form:

Q: Determine the equation of the tangent line to the graph of y = f'(x) at the point where x = 1 if…

A:

Q: Suppose that the instantaneous rate of change of f at the point (3, 2) is 5.  Which of the following…

A: Given, The instantaneous rate of chang of f at the point (3,2) is 5.

Q: For f(x)=x^4, the instantaneous rate of change is known to be -4 at x=-1. Find the equation of the…

A: Given that: *The function f(x) is f(x)=x4. *The instantaneous rate of change is the slope of the…

Q: For the function y = (x - 5)(x2 - 3x + 1) at (2, -3) find the following. %3D (a) the slope of the…

A: We have to find slope of tangent line and instantaneous rate for change..

Q: If the instantaneous rate of change of f(x) at (4, −3) is 7, write the equation of the line tangent…

A: The objective is to find the equation of the tangent line to the graph of f(x) at x=4.

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: 3. For the function g(x) = x' - 2x -1, at what tangent point is the instantaneous rate of change…

A: Instantaneous rate of change of f(x) at x=a is given by f'(a), where f'(x) is the first order…

Q: if x=t^2+1 and y=t^3, then the second derivative is?

A: x=t^2+1⇒dx /dt​=2ty=t^3⇒dy/dt = 3t^2​

Q: Find an equation of the tangent line to the graph of y=e^-x^2 at the point (2,1/e^4)

A:

Q: For the function P(x) = x³ - 7x, at the point (2, -6), find the following. (a) the slope of the…

A: Note: The instantaneous rate of change is the slope of the tangent line at a point.

Q: Find the slope of the tangent to the curve y2 ln(x) + x2y = 7 at (1, 7)

A:

Q: If the instantaneous rate of change of f(x) at (9, -7) is 6, write the equation of the line tangent…

A:

Q: For f(x)=x^3​, the instantaneous rate of change is known to be 27  at x=3. Find the equation of…

A:

Q: For the function y 6x + 4x + 6, at the point x = 4, find the following. %D (a) the slope of the…

A:

Q: 12) Find the equation of the line tangent to g(x) = (3x + 11)ex-4 at x = 4.

A: ddxuv=vddxu-uddxvv2

Q: x + y + xy = 21

A: The function is given as , x+y+xy=21 find the second derivative.

Q: 2. Find the equation of the tangent line to the graph of f(x) = 3x?e-1 - 1, at r = 1.

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 12 e* +…

A:

Q: For the functiony = (x2 + 2)(x3 − 4x),at(−2, 0)find the following.(a) the slope of the tangent…

A: y = (x2 + 2)(x3 − 4x) = x5 + 2x3 - 4x3 - 8x = x5 - 2x3 - 8x Recall famous law of differentiation:…

Q: 9) Find the equation of the tangent line to: y = (1+x) e*when x=0

A:

Q: If the instantaneous rate of change of f(x) at (6, −8) is 4, write the equation of the line tangent…

A:

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

A: Given: f(x)=e-xln(x)

Q: For the function y = (x2 + 2)(x3 - 9x), at (-3,0) find the following. (a) the slope of the tangent…

A: The given function is y=x2+2x3-9x. Differentiate fx with respect to x.…

Q: 2 2х + 2х +1 G(x) = Jsech(x) y e dy

A:

Exponential Growth Model

The relation that represents an exponential function is: