Find a and b such that the function (2? + 6ӕ + 5 if x<1 lax + b f(x) = if x > 1 s differentiable everywhere.

Q: Find values of the constants a and b, that make the function f(x) continuous everywhere. (2x3 + x +…

A:

Q: 8. Iff and g are differentiable at xo such that f(xo) g(xo), prove that each of the functions h =…

A: (8) Given that f and g are differentiable at x0 such that fx0≠gx0.Also h=minf,g and H=maxf,g. To…

Q: 3. If f is continuous and f (x) dx = 8, show that the graph of ƒ intersects the line y = 4 at least…

A: The function f is continuous. The integral function is ∫13fxdx=8.

Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

A: Given   y = sin (x3) ....(1)   , (1, 2)

Q: Find the absolute maximum and absolute minimum values of f on the given interval. a)…

A:

Q: тт Find the absolute minimum and maximum of f(x) = 2 sec x tan x on the interval [-- 4' 4

A:

Q: Let ƒ(x), g(x) be two continuously differentiable functions satisfying the relationships ƒ′(x) =…

A: Given,

Q: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 16 over the interval [1, 4].

A:

Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: 5) Find all possible oblique asymptotes for following functions: y = Vx² + 1 2x/2+2x-3 y = Vx+1 y =…

A:

Q: 3. Given f(x) = x³ + x² – x + 1, on the interval bsolute maximum and minimum values, and indicate…

A:

Q: If f(x)= 2- cos(x) sin(x) then the absolute minimum of f on the 3T interval | 프,프15: 4 O 2/2-1 O…

A:

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: The domain for the function ex y = x ln(3 - x) is {x/x 3} O

A:

Q: if I 2 1. Determine the constant k such that the function f(r) is continuous at I = 2.

A:

Q: The function f(x)= (x² – 1)³, is decreasing on the interval (- 00 , – 2) U (0,2) ^O (-1,0)U (1, ∞o )…

A:

Q: If f(x) =- 2-cos(x) sin(x) then the absolute minimum of f on the TI 3T is: interval O 2/2-1 O 2/2+1

A: Steps to find the absolute minimum value : Find the critical point of f Evaluate the function…

Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

A:

Q: Find the maximum and minimum values of the function f(x) = x – sin x on [0, 27). %3D

A: The given function is: f(x)=x-sinx For maximum and minimum value, differentiate the function and…

Q: On the graph of f(x) = cos x and the interval [-2n, 0), for what value of x does f(x) achieve a…

A:

Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

A:

Q: If G(x,y) is differentiable with respect to x and y then it is always possible to find the number…

A:

Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

A:

Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: y=x-4x The domain of given function is [0, ∞). Differentiating with respect to x, we get…

Q: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

A:

Q: At which point does f(x)=2sinx-cos the maximum value over the interval [0.2 * pi]? 2x have an…

A: f(x)=2sin(x)-cos2(x) f'(x)=2cos(x)+2sin2(x) Now to find the critical number, f'(x)=0

Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

A:

Q: Show that the function is differentiable at x=0 and find f'(0). f(x) = x2sin(1/x), if x is not…

A:

Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

A:

Q: Find a value of the constant k, if possible, that will make the function continuous everywhere. (kx…

A:

Q: Find the absolute extreme values of the function on the interval. 14) f(x) = ex - x, -1 sxs 2 %3D

A:

Q: Let be a differentiable function such that f(3)=2.345 and f'(x)= ln(x^2+1).What is the value of…

A:

Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

A:

Q: Let P=(x,y) be a point on the graph of y=square root of x a) Express the distanced d from P to the…

A: Please refer to the image below.

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

A:

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

A:

Q: Find the value of k that makes function continuous at I = 4 2x + 8 x > 4 f(x) = 4x k r< 4

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

Q: function, that is 0 everywhere except at t=0, is know as:

A:

Q: f(x)=12+4x-X ', [o,s]

A: We will use derivative test to find the maxima and minima.

Q: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: Show that there exists an x in the interval (0, 1) that satisfies the given equation V = 1-x Hint:…

A:

Q: 1. f(x) = x2 + x – 1 for all values of x %3D

A: A detailed solution is given below