surface example
3D Two Peak Surface Graph
Two smooth hills separated along the x-axis.
z = exp(-((x - 2)^2 + y^2)) + exp(-((x + 2)^2 + y^2))Teacher prompt
How many main local peaks are visible?
There are two main peaks, one near x=2 and one near x=-2.
min z 0.00max z 0.0056 samples
What this graph represents
Each exponential term contributes one mound.
Where it appears in calculus
Useful for optimization landscapes with multiple local maxima.
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Open another surface page and compare shape, slices, and contour behavior.
Saddle Surface
z = x^2 - y^2A saddle surface curves up in one direction and down in the perpendicular direction.
Gaussian Surface
z = exp(-(x^2 + y^2))A smooth bell-shaped surface centered at the origin.
Elliptic Paraboloid
z = x^2 + y^2A bowl-shaped surface that opens upward.
Inverted Paraboloid
z = 12 - x^2 - y^2A dome-shaped surface with a highest point at the center.