Find the coordinates of the minimum point of the curve y=2x2+1.

Find the coordinates of the minimum point of the curve y=2x2+13.

minimize f (x,y) = 2x 2 1 + 2x 2 2 −20x1 −12x2 + 65 using simplex method with initial points x 0 = (3,4) and x 1 = (3,6)

What is the equation of the tangent to the curve:𝑦=𝑥2−1𝑥2+1y= x 2 +1x 2 −1​ y, equals, start fraction, x, squared, minus, 1, divided by, x, squared, plus, 1, end fractionat the point where 𝑥=1x=1x, equals, 1?

Find the centroid of the region bounded by the curve 𝑦 = 𝑥 2 y=x 2 , the 𝑥 x-axis, and the lines 𝑥 = 0 x=0 and 𝑥 = 1 x=1.

Consider the function 𝑓(𝑥)=𝑥4−4⋅𝑥2. Find the relevant curve sketching information and then select the correct graph from the list below.𝑥-intercepts: {−2,2} Enter your answers inside curly brackets, e.g. {1,2}𝑦-intercept: 0Relative minima: [𝑥,𝑦]= Enter your answer as an ordered pair inside square brackets, e.g. [1,2]. If there is more than one relative minimum, enter your answers inside curly brackets, e.g. {[1,2],[3,4]}.Relative maxima: [𝑥,𝑦]= Enter your answer as an ordered pair inside square brackets, e.g. [1,2]. If there is more than one relative maximum, enter your answers inside curly brackets