Q2: By the false position method, find approximation value of the root for f(x) = ex - 2 with & =0.0005

Q: Use the first derivative test to find the location of all local extrema for .3 f(x) = +4x*+7х— 5 3

A: For extreme values we find critical points by putting f'(x)=0

Q: Find a rational (fraction) approximation for the value of 3√11 (square root 11, it wouldn't go…

A: We know that linear approximation (by using the tangent line to f(x) ) of f(x) at point (a,f(a)) is…

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = a - 3x + 2

A:

Q: -Find the range of the function y = 2 - sin3x

A: Introduction :

Q: Find the smallest positive root for the given function by using secant method. S(x) = 4 In(x') – x²…

A:

Q: Use the chain rule to find the derivative of 13 f(x) = 3(6x* – 5a³)* You do not need to expand out…

A: Given that:f(x)=36x4-5x313To find f'(x)

Q: Determine the root of the equation x3 – e–x  + 4 by two open methods and round-off your answers to 3…

A: The given equation is: fx=x3-e-x+4 Two open methods are: Newton's method Secant method

Q: Solve for the root (5 decimal places) of the following equations using: A.) Incremental Search…

A: We are given f(x)=1.1288x-sinh(1.3288x)=0 x0=0.5, ∆x=0.1 ,TOL=0.001 Step x f(x) 1 0.5 0.51227…

Q: What is the y-coordinate of the y-intercept of the secant line of the square root function at x=1…

A: Here we have to find the y-intercept of the secant line

Q: Find the x-coordinates of all local maxima using the second derivative test. p(x)=x7+4x6+10

A: Again differentiating with respect to x, we get

Q: Find the critical points and apply the Second Derivative Test (or state that it fails):  f (x) = 3x4…

A: fx=3x4-8x3+6x2 Differentiating with respect to x, we get f'x=3·4x3-8·3x2+6·2x=12x3-24x2+12x Again…

Q: 2- Find the approximate roots of the following equation f(x)= 4x – x² -2 = 0 on [0,1], by using…

A: According to the given information it is required to find the approximated roots of the equation…

Q: After two iterations using the Method of Successive Substitutions, what is the root of f(x)= 3x +x'…

A:

Q: Use the fixed point method to approximate the root of the equation 10* –13.x-9 0 in the interval…

A: Consider the given equation whose root is to approximate using fixed point method.

Q: Q1)) Find the root of f(x) =x – 3 by False position method with the interval [1,2], for three…

A: Given :  f(x) = x2 - 3  Here x2-3=0  Let f(x)=x2-31st iteration :Here f(1)=-2<0 and f(2)=1>0∴…

Q: Jx + 2x f(x)=- 7х — 4х? 8.

A:

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = 2° – 3x7 +2

A:

Q: Use the second derivative test to find the local extrema for the function. y = 3x5- 25x3 + 60x + 20

A: We can use the application  derivative in order solve the given problem.

Q: Use the false position method to find a root of the equation (e power x) +(2 power −x) + 2cos x = 6…

A:

Q: 5. Iny+ea²²x+y = 10 -

A: The given equation is lny+ex2y2-x+y=10. Find the derivative of the equation. Here we use the…

Q: use Newton-Raphson method to obtain a root of equation x'-5x+3=0

A:

Q: If Newton's method is used to find a root of f(x) = (x – 3)7 = 0, -

A: In this question, we have to check the convergence for a given  function  by newton method.…

Q: Q8.) By using the definition of the derivative, find the equation of the tangent line to the graph…

A: Please see the answer in Step 2

Q: I Pind the root of the function byusing Newton- Raphson method) with Xo1,where fcx> = x²_5x +6

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

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: Find a root of an equation f(x)=2x3-2x-5 using Newton Raphson method

A: We will find out the required root.

Q: Find the root of the equation using any bracketing method: f(x) = x2 – sin x - 0.5 with an upper…

A: Bisection Method:This is one of the simplest and reliable iterative methods for the solution of…

Q: The higher derivative of y = 5x³ – 2x is O 15x2 – 2 О 30 O 30x

A:

Q: V/2x+3) (x²+1)" 17. f(x)=-

A:

Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: (B) Use the first derivative test to find the maxima and minima for f(x) = 3. 5z2 + 6x +9. 2.

A:

Q: find the critical points and apply the Second Derivative Test (or state that it fails).…

A:

Q: Find the anti-derivative of  s(x)=−7x2.  (Do not include the constant C in your answer.)

A:

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

A:

Q: 2) Use the second derivative test to find the local extreme values of y= x5 – 5x³+7

A: Given that, We will find the local extreme values of the function as following.

Q: The slope of the tangent line to f(x) = 3x² – 1 at x = 2 is 12. true false

A: The solution of the problem is given in the next step.

Q: Find X values of all points on the graph of g=x²³ + 3x² -11x +5 where the slope of tangent line is 3…

A:

Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=O?

A:

Q: Find an estimate for the positive root of x³-x²-x+1=0 using seven iterations of the Fixed-Point…

A: The following steps are used to find the numerical solution of the equation fx=0 by the fixed point…

Q: 2. Estimate the root of the expression, f (x) = 8 – 4.5(x – sin x), using False-Position Method in…

A: Here f(x)=8-4.5⋅(x-sin(x)) 1st iteration :Here f(2)=3.091838>0 and f(3)=-4.86496<0∴ Now, Root…

Q: Find the tangent line to the equation: f(x) 3x2 + 2x-1, when x= 2 %3D

A: Using equation of tangent formula.

Q: The equation of a curve is y= 4x²+4lx+12-k, where kis a constant. In the case where k=1, find the…

A: If a line is parallel to the x-axis then its slope will be 0.   Slope of the curve y=f(x) is m =…

Q: The vertical distance covered by a rocket from t 5 to t 30 is given by %3D 30 150000 2000 In 2100r -…

A: Given :-  The vertical distance covered by a rocket from t=5 to t=30s is given by  x = ∫5302000…

Q: At what point on the parabola y=3x^2+2x is the tangent line parallel to the line y=10x-2? Use first…

A: We have to find the point.

Q: Q 4. Use ab-initio method and find the derivative of 3x +5x² – 2x-12.

A: ab-initio method is nothing but differentiating the function using basic principle of…

Q: Q3\ Find the second derivative of the funetion F(x)= 3x + 2x - 6x2 -4

A: