ƒ(X) = ||X||, XER¹. For X 0 and e any unit vector, show that Vef(X) = (X, e) ||X||

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: An equipment currently worth $15,549 is expected to be worth $12,704 in 5 years. Assuming linear…

A: Here, given that the equipment is currently worth $15,549 and is expected to be worth $12,704 in 5…

Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A:

Q: Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval…

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: Consider a function f: R? → R°, the derivative of f isa O 3 x 3 matrix O 3 x 2 matrix O 2 x 3 matrix…

A:

Q: The acceleration of an object after t seconds is given by the vector-valued function a(t) . | If…

A: to find the velocity equation, take integration  .............(1)

Q: g(x) = V4t + 5dt. Find g'(2). Let 3-x

A: We have given that  gx = ∫3-xx24t+5dt We have to find g'2 for that we have to use Leibniz integral…

Q: determine f ∗g. Q. f(t)=t2, g(t)=et

A:

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

A:

Q: The graph of ax + b f(x) = (x+ 1)² has a horizontal tangent line at (-2, –1). Find a and b.

A: Given,           The graph of fx=ax+bx+12 has a horizontal tangent line at -2,-1.

Q: determine f ∗g. Q. f(t)=t, g(t)=1.

A:

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: Give two distinct linear functions ƒ and g that satisfy ƒ'(x) = g'(x); that is, the lines have equal…

A: It is given that fx and gx two distinct function.

Q: Find the derivative of f (t) = (6t3³ - 8t² + 7) 46 f' (t) = BA

A: Given query is to find indicated derivative.

Q: Let u and v be the linear functions defined asu(x)=2x+3,v(u)=3x-2.Find the compositions u*v and v*u.…

A: For uov, we do u(v(x)), and for v o u, we do v(u(x)) .

Q: Find the gradient of f(m, n) = m³ +n³. grad f = i +

A:

Q: Determine the position function, s(t),

A:

Q: Use linearization to estimate v26. Use L(x) = f(a) + f'(a)(x – a), where f(x) = vx and a = 25. Once…

A: Linearization formula L(x)=f(a)+f'(a)(x-a)

Q: Let f(x) : x4 Find all values of I such that the slope of the tangent line is - -4.

A: The given function is fx=1x4 and the slope of the tangent line is -4.