Question 3. Consider the function: f(x, y) = 1 + ln(2x + y) a) Show that...

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Question 3. Consider the function: f(x, y) = 1 + ln(2x + y) a) Show that f is differentiable at (1.3). b) Find the linearization of f at (-1,3) and write down an equa- tion of the tangent plane to the surface z = f(x, y) at the point (-1,3,1). c) Use the linearization of f at (-1,3) to approximate f(-1.1, 3.05). d) Using differential, estimate the change in f as we move from P(-1,3) to Q(-1.1, 3.05). e) Find the value of the constant "c" so that the normal line to the surface f(x, y) = 1+ln(2x+y) at the point P(1, 3, 1) passes through the point Q(c-1, 6, -2). Question 3. Consider the function: f(x, y) = 1 + ln(2x + y) a) Show that f is differentiable at (1.3). b) Find the linearization of f at (-1,3) and write down an equa- tion of the tangent plane to the surface z = f(x, y) at the point (-1,3,1). c) Use the linearization of f at (-1,3) to approximate f(-1.1, 3.05). d) Using differential, estimate the change in f as we move from P(-1,3) to Q(-1.1, 3.05). e) Find the value of the constant "c" so that the normal line to the surface f(x, y) = 1+ln(2x+y) at the point P(1, 3, 1) passes through the point Q(c-1, 6, -2).