Suppose that f(x) = (2x – 5)°. (A) Find an equation for the tangent line to the graph of f at a = 2. Tangent line: y = (B) Find the values of a where the tangent line is horizontal. If there are no such values, enter -1000. Values of a = %3!

Q: If the slope of the tangent line to the graph of y%3f(x) at x-Da is m(a)%=D2a+1, and f(1)=5, then…

A: Given: If the slope of the tangent line to the graph of y=fx at x=a is ma=2a+1and f1=5. To Find: f2…

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: Show that an equation of the tangent line to the graph of =D2 at the point (a, b) is given by 2. b…

A: It is given that, Now take the derivative of the given function with respect to 'x'. Therefore,…

Q: Find an equation of the tangent line to the graph of the function                      y = arctan…

A:

Q: (a) If F(x) = 6x/(2 + x2), find F '(2) and use it to find an equation of the tangent line to the…

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 fl-1)=2, then what…

A:

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

A: slope , m=dydx.

Q: 5. Find the slope of the tangent to the function b hor-0-s1= -S= xb 6 Ⓒ-(²-x) at x=1 Yo For-V xb

A:

Q: Find an equation of the tangent line to the graph of f (z) = -2² + 3z – 2 at the point (2, 0)

A:

Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

A: Given, y=2-x3 Point P = (1, 1)

Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

A:

Q: If y = Vr² + e(1-2), the slope of the tangent line to the graph of y at a = 0is

A:

Q: 2) Find the equation of the tangent line to the graph of x? + (y – x)3 = 9 at the point x = 1.

A:

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 – x? –…

A: Given:    y=4-x2-ln12x+1 at (0,4)   We are given that x0=0   The value of function at given point…

Q: y = x^2+ 1, find an equation of the tangent line to the graph of y at x = 3.

A:

Q: Find the equation of the tangent line to the graph of f (x) = x² – 3 at the point (3, 6). Answer y =

A: Find the equation  of the tangent  line to  the graph  offx=x2-3   at the point  3,6Answer:We  have…

Q: Find the equation of the tangent line to the graph of y = x² + 2e* at the point (0, 2).

A:

Q: Find an equation for the tangent line to the graph of y – 3xy + x2 +1 = 0 at the point (2, 1).

A:

Q: Given: f(x)=x2+2 find the equation of a line tangent at point P(1,3) using limits

A: To find the equation of a line tangent at point P(1,3) on below curve using limits.

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 tangent line to the graph of y =f(x) at the point where x=-3 if f(-3) = 2…

A:

Q: What is the slope of the tangent line that touches the graph of In y + e2z-1 = 3y – 4x at the point…

A: Given that: lny+e2x-1=y-4x

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

A: Solution:Given          f(x)=sec-1(ex);              (ln 2, π/3)To find the equation of the line…

Q: (c) Find an equation of the tangent line to the graph of x2/3 + y2/3 = 5 at the point (1,8).

A: Given: The equation of the graph is  x23 + y23 = 5 To find: The equation of the tangent line to the…

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

A:

Q: Find an equation for the line tangent to the graph of f(x)=−2xe^x at the point (a,f(a)) for a=2.…

A: Find the derivative for f (x). Find f’(x) at x = 2.

Q: Find h'(-1) if h = fog, f(x) 3x2 8 and the equation of the tangent line of g at --1 is y = -2x +7.

A:

Q: y = 3x?+1 ; (0,1)

A: Solution ) slope of the tangent line by the limit definition = m = (dy/dx) [ x = 0 becuase we have (…

Q: Let f(x) = 5x + 20x². Then the equation of the tangent line to the graph of f(x) at the point (2,…

A:

Q: 8. Find the constant "k" such that the slope of the tangent to y = 12e-2.3x+k is equal to -4 at x =…

A: 8. Given Data: The equation of the line is: y=12e-2.3x+k The slope of the tangent to the given line…

Q: 4. Find the equation of the tangent line of the graph of f(x) = 12/T – 16 at the point where the…

A:

Q: B - Find the point on the curve y = x3 + x2- 1 where the tangent parallel to the x- axis.

A: Topic- slope of tangent and application of derivatives

Q: What is the slope of the tangent line that touches the graph of In y + e2"- = 3y – 4r at the point…

A:

Q: Find the equation of the tangent line to the function f(x) = -3x – 2x2 – 1 at the point where x =…

A: Given : fx = -3x3 -2x2 -1

Q: Find h'(-2) if h= fog. f(z) = 372 + 8 and the equation of the tangent line of g at-2 is y= 4x 6.

A: Here we have to find h'(-2) if h=f∘g , g(x) =3x2+8 and the equation of the tangent line of g at -2…

Q: a. Compute the derivatives of the following function: sec(xy) = 4x(3x+ 5)5 b. Find an equation for…

A: Product Rule of differentiation : d(u.v)dx=u.dvdx +dudx.v dxndx = nxn-1 Equation of line passing…

Q: Find an equation of the tangent line to the graph of y=e^-8x at the point (5,e^-40)

A: To find an equation of the tangent line to the graph of y=e-8x at the point (5,e-40).

Q: Q3)B/ Find the slope of the tangent line to the graph of x² cos(y) = 2y- eš* at the point (1? %3D 00…

A:

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

A: Given query is to find the slope of the tangent.

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: Find the equation of a curve passing through 1, if the slope of the tangent to the curve at 4 any…

A: The slope of a tangent line to a curve and point on that curve are given. From these information, we…

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: Q5. Find the slope of the tangent to the curve Xy+x-y37+x at the point (1, 2).

A:

Q: Find f (4) and f ,(4) if the tangent line to the graph of f at x = 4 has equation y = 3x − 14.

A:

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.…

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: