Find the linear approximation to the following functions at the given point a. ƒ(x) = x3 - 5x + 3; a = 2

Q: Find the values of x for which  f(x)=(1/3)x3 +(5/2)x2 +6x-17 Has a tangent line that is parallel…

A: As the line is parallel, slope of them will be equal. Slope of f(x)=x33+5x22+6x-17 will be :…

Q: Find the derivative of the following functions and simplify:  a. f(t) = (2t2 + 5t + 1)(3t - 4) b.…

A: Consider the first function: ft=2t2+5t+13t-4 Differentiate ft with respect to t:…

Q: 2x+1 S(x) = 3x+2,

A: Solution:Given     f(x)=2x+13x+23To find the derivativeFormula:ddx(xn)=nxn-1uv'=vu'-uv'v2

Q: Find the derivative of the function. (S h(x) = %3D 8x2 + 9

A:

Q: Find the derivatives of the following functions: 1. y = 2x3 + 6x 2. y = 7x* - 3x? 3. y = (3x +1)(2x…

A:

Q: Find an equation for the line tangent to the graph of the given function at the indicated point. x2…

A:

Q: Find the slope of the following implicit functions at the given points. |v² – 4xy| – 4 = 0 at…

A:

Q: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

A: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

Q: Graph the function f(t) = (/t, 2t +1) by eliminating the parameter.

A:

Q: The second derivative , for the function 7y+ 13z 3a2 is O y = 9

A: Given query is to find the second derivative of the function.

Q: w = (2x – 7)(x +5)/ Establezca dw dw dx 2.

A:

Q: .Find derivatives of the following functions a) f(r) = -r' + 6x² – x² + 5.3r + v10 b) w(s) = s'(7s +…

A:

Q: Find the derivative of the following function. y = In(6x² – 7x) – 4x А) 18х? -7х x(6х* - 7) В) 1 - 4…

A:

Q: Find the linear approximation to the following function at the given point a.

A:

Q: Find the equation of the tangent line at y = 0, given the inverse function x (3y + 2)(y+1)2. x - 7y…

A:

Q: Find an equation for the line tangent to the graph of f(x)=−7xe^x at the point (a,f(a)) for a=2.

A: Given:

Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

A:

Q: Find the derivative of each function defined as follows: 1. m(t) -6t(5t* – 1)* 2. y = (x³ + 2)(x² –…

A: As you have asked for question numbers 4 and 5 only, so I am solving those only. Thank you.   We…

Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 & f/0=e0=1

Q: For the function f(x) = 4x² + 2, the slope of the tangent line at x = 3 is a m = 32 b m = 4 m = 8 d…

A:

Q: Find the linear approximation to the following function at the given point a. ƒ(x) = 9(4x + 11)2/3;…

A: To find the linear approximation of the following function at the given point a. f(x)=9(4x+11)23,a=4

Q: f(x) = x², with 0 < x < 6

A: Length of the curve y=f(x)  from   x=a to x=b   is give by  L=∫ab1+dydx2 dx

Q: Find an equation of the line tangent to the following curve at the point (a,f(a)). f(x) = 8 ex + 5x;…

A:

Q: (b) Write the equation of the line tangent to the graph of f(x) at z 1, and graph it below f(x) =…

A:

Q: Find the derivative of the following function. f(x) = - 3e X-7 e 4x - 2 ex ..... (-3e -x-7e 4x-2 ex)…

A:

Q: Given that f(−2)=−8f(−2)=−8 and f′(−2)=−7f′(−2)=−7, find an equation for the tangent line to the…

A: Given : f(-2) = -8, f'(-2) = -7   To find the equation of the tangent line to the graph of y= f(x)…

Q: Compute the derivative of the given function. f(x)=−4x^π+4.1x^1.3+π^1.3

A:

Q: Find an equation for the line tangent to the graph of  f(x) = 6xex at the point (a,f(a)) for a =3

A: To write down the equation of the tangent to the curve at the given point

Q: Find the relative maximum and minimum values. f(xy) = e 6x2 + 4y2 + 8

A:

Q: e. Find the point(s) on the graph of f(x)= 5x³(4x² – 60) that have horizontal tangent lines. |

A: Any function have horizontal tangent line at points where derivative is zero

Q: Given that f(3) = -1 and f'(3) = 5, find an equation for the tangent line to the graph of y = f(x)…

A:

Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)³ 5. h(x) = 2-9, 3 x+5 %3D 6. A(x) =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the derivatives of the functions s = ( 4t/t + 1)-2

A: Given function - s = 4tt+1-2s = t+14t2s = t4t+14t2s = 14+14t2s = 142+14t2+21414t…

Q: Find the derivative of the given function a. y= (2x-3 / 5x+1)4 b. 6x2-11x-x3+6 / -4x2+x+x3+6

A:

Q: Find the first and second derivatives of the functions s = t2 + 5t - 1/t2

A:

Q: Find an equation for the level curve of the function f(x,y) that passes through the given point.

A: The given function is,

Q: 3 f(x) = x2, with 0 < x < 1

A:

Q: Find the derivative of the following function. x4-3\1/2 x2 +5 25 + 10x3 +3x y' 3= (22 + 5)2 None of…

A: To find the derivative of the given function.

Q: of the function. + 3y + 11

A:

Q: f(x) = + 2x' with 1 < x< 2

A: Given: fx=x36+12x with 1≤x≤2

Q: Use the sign pattern for the derivative dƒ/ dx = 6(x - 1)(x - 2)^2(x - 3)^3(x - 4)^4 to identify the…

A:

Q: Find the derivative of the function C=25(11q^5−14)^8.

A: According to the differentiation rule the power comes down and reduces by one and then chain rule is…

Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

Q: Find the derivative of the following function. f(w) = 8w° + 5w* + 4w %3D f(w) =D

A: We can find the derivative as below

Q: Find the linear approximation to the following functions at the given point a.

A: Since, Linear Approximation is defined by the given formula:-L(t)≈g(a)+g'(a) (t-a) -(i) Where g (a)…

Q: Find f(x) if y = f(x) satisfies dy 35yx4 dx and the y-intercept of the curve y = f(x) = = f(x) is 2.

A: In this question we have to find f(x).

Q: For  f(x)=(2x−3)3, find the equation of the tangent line at x=0 and x=2.

A: Given the equation of the curve, f(x)= (2x-3)3 To find the equation of the tangent line at x=0 and…

Q: For the function f(z) = ¹, the point z 1-e Z = 0 is

A:

Q: f (x) = Vx³ – 3x7 + 2

A: We can find the derivative as below