On the contour plot, clearly mark with a diamond the point(s) of the level curve at which ♦ and . On the contour plot, clearly mark with a heart the point(s) of the level curve at which the ♥ slope is shallowest ( is small). Beginning at point clearly sketch the path of steepest ascent. A, (8 pts) Use the table of values of to estimate the following: 1 1.2 x \ y 2 6 6.1 2.1 6.31 6.52 Approximate Approximate Use (a.) and (b.) to estimate Use (c.) to estimate the directional derivative of at in the direction of . f (10 pts) Find the linear approximation of at and use it to approximate . (10 pts) Assuming that in the equation we define as a differentiable function of use the y x, multivariate chain rule to find at the point .
On the contour plot, clearly mark with a diamond ♦ the point(s) of the level curve at which and . On the contour plot, clearly mark with a heart ♥ the point(s) of the level curve at which the slope is shallowest ( is small). Beginning at point A, clearly sketch the path of steepest ascent. (8 pts) Use the table of values of to estimate the following: x \ y 1 1.2 2 6 6.1 2.1 6.31 6.52 Approximate Approximate Use (a.) and (b.) to estimate Use (c.) to estimate the directional derivative of f at in the direction of . (10 pts) Find the linear approximation of at and use it to approximate . (10 pts) Assuming that in the equation we define y as a differentiable function of x, use the multivariate chain rule to find at the point .
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