a)Fit a curve of the form f(x) = Db-2.4 3.r to the following data -0.5 3.5 6.9 f(x)- -1 2.5 5 8.3 9.2 22.

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: a)Fit a curve of the form 1 S(x) = Db-2.4 to the following data -0.5 3.5 5. 5 6.9 f(x) -1 2.5 8.3…

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Q: Find the equation of the tangent line to the graph of f(x) at the given point. f(x) = V12x + 4 at…

A: The function is fx=12x+4 and the point is given as 1,4. Differentiate the function with respect to…

Q: The tangent line to y=f(x) at (2/(2) is line through given point whose slope is equal to (a) f (a)…

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Q: Let f(x) = 6x + 2 tangent line to the graph of f(x) at the point (0, – 3) is given by y = mx + b for…

A: The objective is to find the equation of the tangent line.

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 all the value(s) of x at which f(x)=(7x^3/3)+3x^2−x+9 has a horizontal tangent line.

A: The values of x at which the given function has a horizontal tangent line can be found by evaluating…

Q: Find the equation of the tangent line to the graph of f(x) = In x at xo = e 8.

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Q: Find the tangent line to g (x) 16 4T at z = 4.

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Q: Find the equation of the tangent line and the normal line to the graph of the function b) f(x) = x…

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Q: Find the equation of the tangent line to f at x = a. f (x) = x2 + x, a = 1

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Q: Find an equation of the tangent line to the graph of y = f 1 (x) at x = 3, where f(x) = x 4.

A: Given: f(x)=x4 at x=3  To find the tangent line of the given function at x=3

Q: Find the equation of the tangent line to the curve f(x) = –a² – 3x +1 at x = 1. о Та) — —3— 5(х — 1)…

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Q: The equation of the tangent line to the graph of f(x)=ln|x at x = -2 is v=²(x+2)+n2 (a) TRUE (b)…

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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: The tangent line to the curve il me f(a) at 2 m 1 goes through the points y=f(x) x == and Find the…

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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: Pls help

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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: Let f'(z) = tangent line to the graph of the function h(z) = g(13x+3) at e and g(x) = f(/#). Let L…

A: Given, f'x = ex2  gx = fx L is the slope of the tangent line to the graph of function hx = g13x+3 at…

Q: Find a > 0 such that the tangent line to the graph of f (x) = x2e−x at x = a passes through the…

A: The tangent to curve at a point is a line that touches the curve at that point and with a slope…

Q: Find the tangent line of f(x) = V1+x at a = 0 and use it to give an approximation for V1.01

A: To find the tangent line of the below function at a = 0. fx=1+x3

Q: Find the equation of the tangent line of e –z = 4x at z = 3.

A: Here we find equation of tangent at x=3

Q: Write an equation of the tangent line to the graph of f(x) 3x at x = +1. %3D 1+2x2 For what value(s)…

A: Given that fx=3x21+2x2 Solution :fx=3x21+2x2f'x=6x1+2x2-4x3x21+2x22if…

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

A: We have given function  fx=e-xlnx Then, f'x=-e-xlnx+e-x1x=-e-xlnx+e-xx Therefore,…

Q: Find the equation for the tangent line to the curve y = f(x) at the given x-value. f(x) = (4x + 5)5…

A: Given equation of curve is as below. To find the equation of tangent line to the curve f(x) at x =…

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: Determine the value of a, given that the line ax+y+1 = 0 is tangent to the graph of y= ax-6x+1 at x…

A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

Q: If y = f(x) has slope  −4  at x = 3, and y value 5 at x = 3, a) write the formula for the tangent…

A: (a) To write: The formula for the tangent line to f(x) at x=3. Given information:  If y = f(x) has…

Q: Find the equation for the tangent line to the curve  y = f(x) at the given x-value. f(x) = ex3 − 1…

A: To find the slope of the tangent at x=1 we have to find f'(1) So, slope = 3

Q: If the slope of the tangent line to the graph of y-f(x) at x-a is m(a)=20+1, and f(1)-5, then what…

A: We have to find function

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: The slope of the tangent to the curve f (x) = 2" at x = 1 is approximately (to three decimal…

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Q: 1. The slope of the tangent line for the function f (x) = In x at x = 1 is: (A) (B) 1 (C) 0 (D) None…

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Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = [(x −…

A: Consider the given function.

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 the equation of the tangent line to the following curve at the given point. y = cosh(x) +…

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Q: If y=mx+b is the equation of the tangent line to the graph of f(x) = X .2 - X at x= -1, then m= b3D

A: According to power rule of differentiation

Q: Find the slope of the tangent line to the given curve at the point corresponding to the specified…

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Q: Find the equation of the tangent line to f(x) = 2 at (3, 1/2). x +1 O y= -1/8x + 5/2 O y-1/2=…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  and the given…

Q: 12 Find the slope of the tangent line, m, of g(x) = 3x2 −2x+ 4 at x = 2 a. m = 12 b. m = 3 c. m = 0…

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Q: Given that the graph of f(x) passes through the point (6, 10) and that the slope of its tangent line…

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Q: f(x)=e*(7x' – 5x² + 2); at x =0

A: Given function: f(x)=ex(7x3-5x2+2) To find the equation of tangent line , find out slope at x=0…

Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = (2x +…

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Q: Find the equation of the tangent line to the curve f(x)=5-x² at x = 2. O x-4y-2=0 O 4x + y +7=0 O 4x…

A: Find the equation of the tangent line to the curve f(x) =5-x^2 at x=2.

Q: Find the slope of the tangent line to the graph of the function at the given point. y = In x3 y 5E 4…

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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.