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- Explain the relationship between the slope and the derivative of fx at x=a.Determine whether each of the following statements is true or false, and explain why. The derivative of a sum is the sum of the derivatives.Where is the function defined by f(x)=ex increasing? Decreasing? Where is the tangent line horizontal?
- At the point (1, −1), the function (x, y) has a derivative of 5 in the direction toward (3, 1) and a derivativeof 8 in the direction toward (1, 6).a) Find fx(1, −1) and fy(1, −1),b) Find the derivative of f at (1, −1) in the direction toward the point (−2, 4).The directional derivative of o = 5x2y – 5y2z + 2.5z2x at the point P(1, 1, 1) in the direction of the line * X-1 2 y-3 = Z -2Find the derivative of the function f(x, y, z) = y y + Z at point (7, -7, 7) in the direction the function increases most rapidly.
- The directional derivative of a function in the direction of ⟨3,4⟩ at the point (1,2) is 1df/dx at the point (1,2) is equal to 5/2.Find the directional derivative in the direction of ⟨3, −4⟩ at the point (1,2)Evaluate the directional derivative of the function f=x^2-y^2+2z^2 at the point A (1,2,3) in the direction of the line AB where B is the point (5,0,4).Find the derivative of the function at the given point in the direction of A. ffx, y) %3D In(6x - бу), (10, -10), А - 6і + $j -1/50 O -3/100 -1/100
- Find a function f so that the maximum rate of change occurs in the direction of u = (1/sqrt(5)) <1, -2> and that the maximum rate of change is 6 at the point (2,-4).At the point (1,−1), the function (x, y) has a derivative of 5 in the direction toward (3,1) and a derivativeof 8 in the direction toward (1,6). a) Findfx(1,−1) andfy(1,−1), b) Find the derivative offat (1,−1) in the direction toward the point (−2,4).Find the first and second order derivative w=3z7-7z3+21z2