Defermine the gradient of the cuirve \( y=3 x^{4}-2 x^{2}+5 x-2 \) at the point \( (48,2) \)

To find the gradient of the curve \( y = 3x^{4} - 2x^{2} + 5x - 2 \), we first need to differentiate it with respect to \( x \). The derivative \( \frac{dy}{dx} \) is given by: \[ \frac{dy}{dx} = 12x^{3} - 4x + 5 \] Now, we take the point \( (48,2) \) to find the gradient at that specific \( x \)-coordinate, which is 48: \[ \frac{dy}{dx} \bigg|_{x=48} = 12(48)^{3} - 4(48) + 5 \] Calculating \( (48)^{3} = 110592 \): \[ = 12 \cdot 110592 - 192 + 5 = 1327104 - 192 + 5 = 1326917 \] Therefore, the gradient of the curve at the point \( (48,2) \) is \( 1326917 \).