Explain why the function has at least one zero in the given interval. C f(x) = x² - 4 - cos(x) [0, π] At least one zero exists because f(x) is continuous and f(0) > 0 while f(z) > 0. At least one zero exists because f(x) is continuous and f(0) < 0 while f(x) < 0. O At least one zero exists because f(x) is continuous and f(0) < 0 while f(z) > 0. At least one zero exists because f(x) being a second degree polynomial must have two real solutions. At least one zero exists because f(x) is not continuous. O Function O Interval

Q: Approximate the fixed point of the function to two decimal places. [A fixed point xo of a function f…

A:

Q: Prove formally that for all a > 0, function af (x) + g(x) is also a concave function.

A: Let’s say we have a function f(x),  If for every value of x, if f”(x) &lt; 0 then the function f(x)…

Q: Let f(x) = ln x and g(x) Show that f(x) and g(x) are both increasing when x > 0. Vr.

A: Given, f(x) = lnx When f(x) is increasing then f'(x) &gt; 0  Differentiating f(x) with respect to x…

Q: Prove that there is no function F that is differentiable everywhere and also satisfies the equation…

A: Give function is fx2+sinx=x we differentiate it, f'x2+sinx2x+cosx=1⇒f'x2+sinx=12x+cosx f'x2+sinx…

Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π. Find any x-intercepts of f(x) on [0,…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.Find any x-intercepts of f(x) on [0, 2π]

Q: Let f(x) = cosx²) and g(x) = vx. The (natural) domain of (f • g)(x) is = Cos

A:

Q: (b) On [0,27) solve f(x) = ½. %3D

A: Explanation of the solution is given below...