12. If fis given by the equation f(x) = 5x² - 4 + In x, what is the slope of the line that is tangent to the graph of f at x 1? %D (A) 7 (B) 8 (C) 10 (D) 11

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

A:

Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

A:

Q: 3. Determine the slope of the tangent at x = -1 on the graph f(x) = (5x² + 1)3.

A:

Q: 4. Write an equation for the line tangent to the curve f(x)=" In(3x) -at x=1

A:

Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

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

A: Given: fx=4xx2+6 We need to find the equation of the tangent line to the graph f(x) at 2,45

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

Q: 14. Find the equation of the line tangent to the graph of f(x) = 2x3-x + 1 at x = -1. %3D

A:

Q: The slope of the tangent line to the graph of the function y = 9Va -2 at (4, 16) is -5.00 O -4.00 O…

A: Simply calculate the derivative of function at given point.

Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

A:

Q: 10. (a) Find an equation for the line tangent to f(x) = x³ + 4x² at the point x = 1.

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Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x is 4

A:

Q: 5) Find an equation to the line tangent to y = (x +3)³ at x = -3.

A: as per bartleby guidelines  i can do only first question. please ask other question seperately.

Q: What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the point.12

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Q: 9) If f(x)= x' – 3x, find the equation of the tangent line at x = 2.

A:

Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

A:

Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 4 if g(4) = −3 and g'(4) = 6.

A: Given that  y=g(x) and g(4)=-3 also g'(4)=6  We have to find the equation of tangent line . Please…

Q: 4. Find the slope of the tangent line to the function f(x)= +3; x+2 at x = 4 5x-10

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Q: 42. At what point on the graph of f(x) = -5x² + 4x – 2 is the slope of the tangent line 6?

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Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: 1) Find the slope of the tangent line to the graph of f(x) = x2 - 3 at the point (2, 1). %3D (8…

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Q: The slope of the line tangent to the graph ofy= xe^ at x =In 2 is A 2 In 2 2 In 2+2 B.

A:

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x = is %3D

A: We need to find slope of normal line.

Q: 1) Find the slope of the tangent line to the graph of f (x) = x3 + x at x = 3.

A: Application of derivative problem

Q: 1. What is the slope of the tangent line to the curve 4x2 - 9y² = 1 at point (3,2) ? b. - 27 8 a. 3…

A:

Q: *(1,). What is the equation of the line that is tangent to the graph of y = at (x³ + 1)?

A: We can find the equation of line as below.

Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-x+1  and f(2)=4, then what…

A:

Q: What is the slope of the tangent line that touches the graph of In(y)+e2x-=3y – 4x at the point (A 1…

A: The solution are next step

Q: 1. Find the slope of the graph of the function f (x) = v3x + 4 at x = 7. Then find an equation of…

A: equation of tangent line is (y-y1) = slope (x-x1)

Q: 3. Find the slope of the line tangent to f(x) = In(4x² – 3) at (1,1).

A:

Q: 3 PROBLEM 2:f(x) at (-1,3) x+2

A: topic - slope of a tangent line

Q: 2х — What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the…

A:

Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

A:

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e - 2x, - 2x 3 fx) 2

A:

Q: What is the slope of the tangent line that touches the graph of Iny+e2x-1 = 3y – 4x at the point A 1

A:

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

A: Given, fx=4xx2+6 Now we find the slope ddx4xx2+6 Now by using the quotient rule,…

Q: 5. Find the slope of the tangent line to the graph of r = 2-2cos e when 0 = に一2

A: We have given equation of graph r=2-2cosθ  We have to find slope of the tangent line to the graph…

Q: 3 Find the slope of the tangent to the graph of f(x) = /x+5 at the point where x= 4.

A:

Q: 4. If f (2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x=2.

A: We have to find the equation of tangent.

Q: 5) Find an equation to the line tangent to y= (x + 3)³ at x =-3.

A:

Q: Show that the curve y = 6 x 3 + 5x -3            has no tangent line with slope 4.

A: y=6x3+5x-3 has no tangent line with slope 4

Q: 4. At what points on the curve y = 2x³ – 3x2 – 2x + 4 are tangents of slope 10?

A:

Q: find the slope of the line tangent tothe graph of ƒ(x) = 5 at P(1, 5).

A: We know the slope of the tangent line to the curve y = f(x) is dy/dx.

Q: Find the equation of the line tangent to the graph of f(x) = (In x)* at x=7.

A: Slope is evaluated by differentiating f(x) wrt x at x=7 . Also f(7) is evaluated. Write equation of…

Q: Find all the points on the graph of y=f(x) at which the tangent line has the given slope.…

A:

Q: True or false, for the graph of y=2^x, the slope of the tangent line is the same as the function…

A: slope of tangent line to a curve y = f(x) is given by          m = dydx

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.