If the gradient of f(x,y) at the origin is (6,8), the slope of the tangent line to the level curve of f through the origin at (0,0) is ___?
I know you have to use a dot product and set it equal to zero. Is it convention or right to assume that f(x,y) = z??
Another question: Shouldn't their be an infinite number of tangent lines at this point or are suppose to assume that the curve is the gradient? Can someone clarify this before my exam at 5?
I know you have to use a dot product and set it equal to zero. Is it convention or right to assume that f(x,y) = z??
Another question: Shouldn't their be an infinite number of tangent lines at this point or are suppose to assume that the curve is the gradient? Can someone clarify this before my exam at 5?
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Yes, because the gradient is normal to the level curve. Hence, the tangent line at (0,0) has the direction of the vetor (a,b) such that (a, b) . (6, 8) = 6a + 8b = 0. The slope is -3/4.
z, or whatever letter you choose, is just a short form for. f(x,y). For example, f(x, y) = x + y is the same as z = x + y.
On the plane there is at most 1 tangent line to a curve at a given point. You don't assume anything, this is a fact.
Not sure if I understood your question.
z, or whatever letter you choose, is just a short form for. f(x,y). For example, f(x, y) = x + y is the same as z = x + y.
On the plane there is at most 1 tangent line to a curve at a given point. You don't assume anything, this is a fact.
Not sure if I understood your question.